Update on my case: I didn’t have any luck with FP support. They asked me to do a number of tests (including the “kicking” the battery as described above), but none of them solved the problem.
I sent them notes and screenshots of the results, which I don’t think they’ve fully read, since I concluded my email saying that I feft this was not normal battery degradation and I got a very short response saying “It’s normal for batteries to degrade over time, but if you feel your battery is not degrading normally please let us know and we’ll replace it”.
When I repeated that the battery was behaving abnormally and described some more tests I had done, they suggested it might be my SIM-card that’s causing the problem. I highly doubt this, but I’ve ordered a new SIM-card just to be sure. However, in the meantime they’ve closed the support ticket before the new SIM even arrived, because I didn’t respond fast enough.
I must say I’m dissapointed with this level of support. To anyone else for who the solutions posted here do not work: if you value your time (and still want to support FP), I would suggest to just order a new battery from the shop. For myself, between the hardware issues and the inability to install custom operating systems, I’m on the lookout for a new smartphone. It’s a shame, since I had really hoped this one would last longer than two years.