No, vanilla JA2 only supports 640x480, but there is an unofficial patch made for vanilla JA2 (this is not 1.13!) that adds support for multiple resolutions, windowed mode, and other technical improvements. It's called Stracciatella.

https://ja2-stracciatella.github.io/download/

Unfortunately, no such patch exists for Unfinished Business and Wildfire as of yet.

Something I don't understand about Stracciatella. When I use the launcher and choose the predefined resolution of 1024x768 or higher, in battles the screen is filled correctly (no black stripes around).

But when passing over the laptop screen there are some pretty annoying black borders, I wonder if it is not a bug.

https://www.dropbox.com/s/ulm0nl43j6uj30o/ja%20strac2.bmp?dl=0

No, filling the screen is not "correct", since with Stracciatella it means a stretched image, which IMO looks much uglier tha black borders. The game was made for 4x3 CRT monitors, not modern widescreen monitors.

If you want true widescreen and for the game to look as good as possible you need to install the 1.13 mod. Unfortunately the full 1.13 is a bit of a mess and rather daunting if you're new to the game, and its Vanilla option is buggy.

Thank you for your answer, and for your explanation, personally I hate version 1.13, so no I don't really want to install this mod, so it's okay.

Is it possible to install just parts of that 1.13 mod?

Otherwise, will Stracciatella work on a, say, 4K monitor as long as the defined resolution is 4:3 (Say, 2666/2000) ?

I'm not sure, and it's been a while since I played JA2.
I don't think you can install only the graphics options of 1.13.
And my experience with Stracciatella was that no matter what I tried it never looked as good as 1.13, but it looked better than vanilla.

Another option may be to try playing vanilla JA2 with something like dgVoodoo - http://dege.freeweb.hu/dgVoodoo2/dgVoodoo2.html - or IntegerScaler: http://tanalin.com/en/projects/integer-scaler/

Hey nice to find you here too (after RPGCodex and CRPGAddict ) :)

I've read somewhere that 1.13 was reasonably configurable, so I have to figure out if I'd rather try that and "take out" the stuff I don't want to play with.

If only I could find out my old saves/installation, I could probably figure out which version I was using on my last attempted playthrough :/