Ha, fuck.. this is likely I've found.
Checked the serial number, and turns out I'm eligible to get the battery replaced for free -
if only the thing wasn't purchased more than three years ago..
So it's a hundred Euros, or about fifty if I go the ifixit route, which looks somewhat complicated..
It shouldn't make any difference, no? If it's a flagged dodgy batch they should replace it anyway... My MBP was over three years old when the screen, GPU and logic board went but the serial number entitled me to free new bits...
I'd try going to a store anyway. If the battery is swollen you could argue it's not safe, and if they already know if's one of a failing batch then they might just swap you for free.
Could be a swollen battery...