Is it possible to update  the battery FW without updating the drone/controller FW?
If so, how is this done?

No, all firmware components are downloaded as a single file and unpacked during the update process. But why would you want to?

Hello and good day nywrecker. Thank you for reaching out and for the inquiry. The DJI Mavic Air's intelligent flight battery is updated along with the said drone's firmware. If there is a need to update the other intelligent flight batteries. Please try to refresh the latest firmware with the drone via DJI Assistant 2. For reference I will post an ofiicial DJI tutorial video on How to Update DJI Mavic Air Firmware with DJI Assistant 2. Thank you.

Punchbuggy Posted at 2-28 14:12
No, all firmware components are downloaded as a single file and unpacked during the update process. But why would you want to?

Many times when I update the FW of the drone or controller new bugs start showing up and got tired of dealing with them or waiting until the new FW is out to fix what the previous one broke.
I learned to live with what I have and dont want to tinker with mostly useless “new features”.