What happens if you only update the drone firmware

[The11thPlague]

I have a Mavic Air 2S produced in March 2021, with stock firmware (no changes).
I'd like to update the firmware to a newer official version, but not to the latest version.

On DDD I can only find drone (aircraft) firmware versions, but nothing for the RC-N1 controller (remote).
If I only update the drone (aircraft) firmware but keep the controller on the old firmware, will they still work fine together?

What about battery firmware?