What exactly is this residue and how do I clean it off?

This is polymerized oil - the same stuff that people build up on iron pans as seasoning.

There is no good way to remove it from a coated surface. It is quite resistant to both chemical and physical methods, as you discovered. Most mechanical methods will scratch your existing coating, and as for chemical methods, the only reliable one is lye. If the existing "nonstick coating" is enamel or teflon, it shouldn't be damaged by the lye, but we cannot tell for sure from a picture.

You can also leave the spot there. The problem is purely cosmetic, it is perfectly well suited as coating for a pan (as said above, it is created on purpose on reactive surfaces).

It might be polymerized oil, which is difficult to remove, but the way it’s smeared on the lower right, it might just be something sugary that dripped and has just caramelized onto the pan.

To see if that’s the case, place it somewhere that it can sit flat, and flood it was water. Leave it for a few hours (or overnight), and then use a plastic spatula or to scrape it gently. If it’s sugars, it should now be loose and come off fairly easily.

If it loosens, but doesn’t come off fully, then scrape off what you can, and leave it to soak some more.

It’s enamel coated re tray, and usually result of engaging self clean oven feature on newer ovens pyrolytic cleaning. Lye doesn’t work IME as these deposits are actually now bonded together. One cannot remove the one without laying waste to other.

You could Try jet/butane torch applied locally for as long as it takes to combust fully…

You might be able to remove it with some strong (and by strong, I mean corrosive to skin, so wear gloves!) oven/grill cleaner such as HG Oven, Grill and Barbecue Cleaner. Best option is to spray it on, put it in the oven and heat it up a little, to about 50C/120F, that makes it work better. Leave for a while, then wipe off with a damp cloth.

Sometimes stuff like this can be removed with a less harsh approach, make a paste of sodium bicarbonate and water, and really go to town with the scrubbing, lots of pressure, perhaps use a nylon brush for a few minutes, you might see it slowly fade and break apart. But that might not work for the toughest residue.

Slice/scrape it off with a razor blade

There are utensils for this, getting one might be easier on the fingers. I do this with the most insisting stains, but do mind your fingers. If you insist on doing it with the blade alone, remember razor blades are flexible, but they do snap in the end. Dont bend it.

If it isn't completely hardened, soaking in vinegar might help, but mechanical cleaning is the best solution.