Macbook air keyboard behaving weirdly when battery is below 99%

My MacBook Air integral keyboard has started doing very weird things shortly after I unplug it from the mains. The battery is showing as well over 90% and the system says my battery health is normal.

More about the problem: some keys don't respond at all, others start behaving as if I'm using weird keyboard shortcuts, e.g. they open obscure menus - or, if I click on an app in the sidebar, the menu opens but I can't open the app. I've checked that I haven't got any weird accessibility options enabled.

If I restart, I can't log in because I can't type in my ID.

It all goes back to normal a few minutes after switching to mains power.

It's an Apple M1 using Ventura 13.2