Heya all, back with the result, as I promised. I wrote support, they’re under a lot of pressure now, so in the end also called them - it might be quicker to call straight away.
They were very helpful and nice, had my phone sent to repair centre for free, where it was immediately switched for a completely new phone and sent back. They can’t say so far what the failure was, but for anyone having a similar problem, it may warrant phone exchange, so don’t be afraid to write. Also probably not a battery issue, I’m concluding.
Thanks for your help to everybody! My new phone is working smoothly, having no issues at all. 