Pretty much any keyboard that's compatible with the nice!nano microcontroller (most boards with a pro micro/elite C footprint). Unfortunately, not sure of many conventional premium boards that let you just socket in your own microcontroller, but there's a ton in the ergo space.

Integrating the battery is easy since you just get taller standoffs for the nice!nano and place the battery underneath. Then, there's the nice!view which is an e-ink screen (great for showing battery level).

As for firmware, ZMK is built with wireless first in mind. It plays very nicely with the nice!nano. Here's a list of supported hardware: https://zmk.dev/docs/hardware#pro_micro.

Here's a low profile Corne that I built recently: https://i.imgur.com/euoETk7.jpg. It's fully wireless with both halves even communicating over BLE!