I recently got a Surface Pro 7 for somewhat similar reasons, and have been pretty happy with it so far. Fantastic in tablet mode with the pen for reading and marking up documents (and reading comics). Perfectly cromulent using the keyboard like a traditional laptop, though there are inevitably some minor trade offs there. Works fine for light gaming too as long as I stick to 2d indie or retro stuff, which is fine since I’ve got plenty of those to keep me busy. Most games do require the keyboard or at least the stylus, but I’ve found a few that are playable in touch-only mode.
I also looked at various 2-in-1 laptops but felt that the keyboard just folding flat rather than detaching would make them clunkier in tablet mode. And I considered an iPad, but decided it was worth dealing with Windows’ less-polished tablet UI for more flexibility and compatibility.
Probably at the high end of your range (I spent $800 on sale at Costco for a bundle with the cheapest i5 model, keyboard, and stylus).