Could you please tell me if there is a way to increase the size of the "battle screen"? I play at a resolution of 1920x1200, and it feels too small.

This question has been answered many times already: to increase the size of battles, cities, etc. (while changing the resolution, and not just stretching the image), it would be necessary to do a huge amount of work to redraw all the interface elements used in these windows. Who would do that?

Alternative solution: play at a resolution of 1181x664 with stretching filters. And you won't have small battle and city windows.
What's wrong with that?

Screenshot:
resolution in the launcher settings: 1181x664
monitor resolution: 1920x1080
https://pp.userapi.com/c639723/v639723186/4d4fc/uCUYyzIzukE.jpg
https://pp.userapi.com/c639723/v639723186/4d57c/nqHrBnixkD0.jpg