Stir-fry pan choices

The wok is a traditional tool for stir-fry, but not necessarily a good tool, depending on your stove-top. It's difficult to bring enough heat to bear on the wok from a flat cooking surface, like almost all western cooktops and ranges have.

A larger wok means that the very flat heat source will have to heat a larger curved surface, much of which curves away from it. All the heat will be concentrated on the very bottom of the dome. There are ways to replicate a wok range on your home stovetop for more even and intense heat, but most of them are spectacularly unsafe.

A decent flat pan that can hold onto a lot of heat will work much better for most home applications. I usually use an enameled cast-iron skillet on the extra-large burner on my electric cooktop, and have had good results with an ordinary saute pan when quickly fine-tuning temperature is desired (seafood, mostly).

A billion Asian households use a thin carbon steel "wok like" device to cook on quickly and efficiently. I have never seen anything work as well, or last as long. Daily use for 20+ years is normal

After the first 10 or 20 uses, the patina is well developed, and they work as intended

Buy one from a Asian food supplier for a few tens of dollars, there is no point in getting a fancy brand name one, it will not be as good

The heat transfer issue, is a factor of your burner. The heat output rating of your burner will dictate how much food you can stir fry at once. If you want to do more at once, you need a bigger burner, not a fancy pan

A comment by @nadjacs is right on the money here: the choice of cooking pans is not your primary method of getting your vegetables to not be mushy. Your vegetables are mushy because they have lost their cellular structure's strength. Part of this comes from the liquid in the cells expanding as it freezes, which damages cell boundaries. Part of this comes from the damage created by heat as it slowly starts to decompose the cell walls. You therefore want to cook these vegetables as fast as possible, and serve immediately.

The first and most important thing you could do would be to defrost the vegetables to get the centers warmer: this can be in a microwave, as long as you do not microwave them until they are hot.(Microwaves tend to be pretty good about heating up the middles of things, as the microwave wavelength is centimeters long or so.)

The vegetables in a stir-fry do not cook principally by heat contact with the pan, but by getting steamed. You want this steam to be as hot as possible to get the vegetables warm as fast as possible. For this, thicker woks tend to be better. My experience with stainless steel woks has been that they're thinner, so they'll lower their temperature faster and give you less-hot steam for stir-frying your vegetables.

As an option over getting a new wok:

Cook the ingredients in batches.

When I'm cooking for a large number of people, I'll cook some onions and some of the firmer vegetables (carrots, broccoli stem, bok choy (non-leafy bits), etc), then move them to a bowl to the side for holding. I'll add another bit of onion (it also acts as a gauge for how far cooked things are), and some of the other vegetables .... then again, put it to the side. Then cook whatever other aromatics you have with the meat, then possibly make a sauce, and mix everything back together (along with the greens from the bok choy, and anything that doesn't take much cooking) for a minute or two for the flavors to meld.

It does take a little bit longer, but being able to get more heat into each batch individual might help mitigate some of your problems with frozen mushiness. (although frozen veg. almost always have a little bit of mushiness)