Do modern ovens bake the same as the old ones? Is the new oven the reason popovers don't rise?

I'd guess it's not the new oven that's wrong, but the old one.

Older ovens has less accurate thermometers & were maybe 20° hotter at the top than the bottom. The chances are your hand-me-down recipe was based on this phenomenon & your new one is accurate… & therefore not hot enough.

I'd never heard of popovers until 10 minutes ago, but reading through recipes online, they seem to be exactly same as Yorkshire Puddings, just served with sweet toppings instead of roast beef & gravy. [How two sides of the Atlantic arrived at that difference, I'll never know nor understand ;)

Most say to use 450°F [230°C] which is more like I'd use for Yorkies - in fact for Yorkies, the hotter the better, preheat your tins too. My rule of thumb has always been, once everything else is done [roast dinner, remember;) just turn the heat to max, add your oil & put your tins in the top half [high as you can but leaving room to rise], then give it 15 mins to come up to temperature. The oil should be smoking before you drop your batter.
Pour quickly & get that door shut. Once in, never open the door until they're ready.

After comments
I've never known anyone to drop the temperature half-way through [but then again, 'crispy' is not something I'd want from a yorkie [only supermarkets & restaurants think they should be crispy, ordinary Yorkshire folks don't]), but I still think you're not getting enough heat into them right at the start.
Maybe your oven really does slump the temperature easily; maybe you've got the door open too long or the element isn't fast enough to get back up to temperature; tins aren't hot enough to start with.

I'd try at least once with the oven simply "on full" - whatever it thinks it can go to - but watch it doesn't switch mode right at the top. if I turn mine full then back it switches to rotisserie/fan grill rather than 'oven'. That might be a little excessive ;)

One thing to check is whether the new oven has "convection" baking features, and if so, if they might be turned on.

My wife and I have an oven with a convection baking mode. A fan blows the hot air around inside the oven. For roasting meats, the convection baking is great; but we have found that for anything baked that we want to rise, we get much less rising when convection is enabled.

My theory is that the convection baking slams more heat into the food more quickly, causing a crust to form, making it harder for the food to rise. This article cites an expert saying pretty much the same thing as my theory:

https://skillet.lifehacker.com/your-convection-setting-may-not-be-the-best-choice-for-1826800725

The new oven is quite likely the reason they won't rise, but I wouldn't say that the difference is strictly on the lines of "old" and "new".

Beside Tetsujin's great point about thermostats being inaccurate, not all ovens bake the same. Even if you are able to reach the same average temperature of the air, the rate of heating for your baked good can vary considerably depending on the physical properties of the oven even with the door closed. Also, when you open the door to place the food in, this interferes with heating, and different ovens can be affected to a different level.

Popovers need to be baked rapidly at a high temperature in order to rise. It appears that your new oven, for whatever reasons, is not heating up the popovers as quickly as the old one. You can try using a higher temperature, or use the usual tricks for increasing the heat exchange rate (preheated metal, or even cast iron molds, using a pizza stone, etc.)

If the newer oven has better insulation than the older oven, then it may have a less powerful heating element to reach the same temperatures (lower wattage). This would also mean that a (relatively) cold item in the oven would take longer to heat up.

You can mitigate this with a "thermal mass", such as a large, flat rock that has been properly cleaned just like any cookware. The large mass of the rock will store thermal energy, and you want it flat to increase the surface area so that it could dissipate that energy quickly.

Depending on the brand and model of your oven, you may have one calibrated with a slow "bounce back" from opening the door.

A few years back, there was a surprisingly expensive Delonghi model that, after you'd opened the door of the oven and put something in, would wait for 10 minutes before it engaged the element to bring the heat back up. I found out about this specifically because friends on another cooking forum bought this model and discovered that they couldn't cook anything that required a lot of oven spring ... like popovers.

I'd suggest researching your oven model, and even calling the manufacturer's tech support line. Also, if you can get an instant-read corded thermometer, like a Thermoworks, and use that to check the temperature of the oven minute-to-minute, you can see how long it takes the oven to get back up to temperature.

One other possible difference between two given ovens, even of the same type, can be how airtight or not they are, creating difference in how moisture is kept or not kept within the oven.

Plenty of good thoughts already, but here's (hopefully) another couple.

First, the multiple temperature process. Given the good chance the oven is not "bouncing back" quickly enough, as FuzzyChef suggested, Setting the higher temp to start, so the oven is hotter when opened, dropping less while open, might help. But instead of backing off for a 15@450/15@350 approach, experiment, holding it longer at 450. I say that since you DID see some rise when beginning at 450. And dropping to 350 when the old standard was 400 throughout kind of sounds more like trying to average 400 overall than a good plan. So when dropping, perhaps shoot for 400, instead of lower.

But there is another thought here, from rackandboneman, about moisture. And that sounds really on target. After all, there is literally nothing in the recipe to make something rise in the oven EXCEPT steam produced inside the popover as it cooks. It would want to push all directions (something that might be useful in other circumstances) but cannot at all downward, and mostly not sideways, so it pushes upward, mostly. That's the rise. What would cause that to be dampened? The moisture not becoming steam. How would that be helped?

Hotter oven, yes, though crusting would limit the effect. A nice top crusting beginning to form would give it a "plate" to push up on instead of puncturing the top like a slow boil would in a tomato sauce's surface, and I wager this is how the crust came to be desired, but too much heat and the sides would begin to harden limiting any rise. The hotter their container to begin with, the sooner that'd be an issue too.

But mostly, it seems that water would "leak out", evaporating or steaming away rather than staying inside and forcing it upwards. One could limit that in a pop bottle but an oven is an open system, basically, with vents so one is limited on using something like a shallow pan, say a cookie sheet, of water that would raise the moisture in the oven's air hoping to lower the rate of water loss in the popover. It could also make the popover surface softer instead of hardening. But then, maybe that's actually the secret to the non-hard Yorkshire puddings mentioned, a higher moisture content in the air... hmmm...

So my suggestion is severalfold. First, raise the preheat to, say, the 450. Experiment with longer times at the 450 before backing it down. Only back it down toward the 400 (not only since some kind of average is not the goal here, but because the old oven was always bottoming out at 400, not lower like 350!). In addition, raise the moisture available, but slowly. Maybe try the cookie sheet thing, but mostly I mean try the regular recipe with the above heating approach and see how it goes. The next time, try adding perhaps a teaspoon of milk to the half cup. Or tablespoon at a time, but a little extra moisture goes a LONG way sometimes (think about how it affects scrambled egges). Use the same heat approach and see if they rise better. My guess is they might.

You can also monitor the temperature to see how quickly it comes back and when it hits 400. Even just a candy thermometer that you can read through the glass gives you a better idea than nothing. When it seems to not plan to go back below 400, that'd be a good time to lower the temp to 400.

Another thought would be, and I don't make these things so I cannot say myself, but to an extent, the warmer the batter can be before entering the oven, the sooner its moisture would start to evaporate or steam so the sooner it would begin rising vs. the sides hardening enough restrict the rise. You want, I believe, the moisture to all lend itself to the rising before leaving the popover, rather than slowly heating and evaporating away without enough expansion beforehand to force the popover to rise. So an non-intuitive thought akin to the old "boil in a bag" foods would be to use a water bath to raise its temp from room temp to at least body temp, or higher if it does not seem to alter the dough's other properties might help as well. Not enough to begin cooking it, but... some experimenting would be needed if you tried it.

The internet seems to think the milk itself can be 125° when added. Hotter and maybe the eggs cook so... but once it's all a batter/dough, it seems like the eggs would have tempered and the extra heating so raise the dough's entire temp might work.

Greasing can affect the idea as well. Not in the sense of arguing should it be shortening, butter, some oil or another, but rather in the sense that grease/oil contains water, with butter supposedly being 20-25% water. A lower water content in the material up against the dough would help more moisture to escape than a higher water content material. Seems a higher water content material might also help against burning the bottoms or sides so perhaps two reasons to consider that. Or it might be negligible vs. the overall problem. One other thought would be moisture is directly available to leave in oils while in greases like butter or shortening, it has to break out of the matrix which might slow its release. That might be helpful too. Lots of people like to use oil rather than "waste" shortening or especially butter.

But try the heat and see. Try extra milk or even just water directly. I bet between the two you're back in business. And then there's warming the batter, more wholly since a water bath could wrap around it like the air in the oven rather than concentrate like a pan's heat, on the bottom. No matter how calibrated controls are, its the heat you actually experience at the food that matters so think about monitoring that to see what affects its moving to a consistent state ("consistent" in that it is smooth at doing whatever it might do, rising or staying stable for a time). The steam inside thing is likely tricky and subject to a tipping point. Monitoring the temp at the product and seeing it stabalize might give you a temp to maintain, or just below. After all, if the steam is all being produced at once at the high end of it, then the slow rise will be less while backing off to a wee bit below that point might keep them steaming longer and so rising longer, and "better."