Dactyl was your first ergo mech? That’s hardcore!

Better site with more profiles: https://www.keycaps.info/

Some boards that use the nice!nano have room to tuck a small battery (I think 110mAh) underneath the controller. If they use the 3 middle pins on the nano though, that’s not an option. Rechargeable coin cells are an option, but for boards with the usual LiPO pouch cells, you’ll probably want some kind of case. Some folks just use double-sided tape to hold the battery to the PCB but I’d rather have some protection.

Height varies a lot between different profiles - check out the comparison on this page (some of those are for low profile switches but G20 and up are for standard MX switches): https://fantechworld.com/keycap-profiles-differences/ Additionally some profiles such as DSA, XDA, and KAM are uniform, meaning every row is the same shape (except for homing keys). Others are sculpted, meaning the height and angle varies between rows.