So not to be that guy that posts stuff that he got resolved and never gave an answer.
I had contact with Apple Support (rather pointless, but friendly to be fair) and the local genius bar business support (they were nice enough even though it was a private phone and happened by accident due to the horrific dial routing they have with all that fancy AI).
A good indicator that your iPhone has no hardware issue is if it activates after a full wipe or reset. Then it is unlikely the SIM module is broken.
Didn't help my case because I had to get my number up asap due to some really important things - so I went on to get a spare non-Apple device to get my number up. By this time I resetted everything twice out of despair and left it wiped for sending it in eventually. But getting my cell up for THE call was more urgent so I left it unattended for like 4h. Then I had to restore my backup again because I needed a TAN and getting the seed this way was much easier than ordering a new QR code. This time I noticed the "no SIM" sign was back on the top of the screen and when I inserted my SIM it worked again and every reboot since then was fine.
What I noticed and ASSUME was the issue in my very own case that setting up another device from scratch with all the updates and patches takes up to 4 hours even on rather stable 100mbps. So longer on 4G/5G propably. Anyhow since I was in a struggle and under stress I might have been too impatient with my resets so the blank software modules for the modem weren't even back up yet... Or it was a very silent patch by ISP to iOS - in which case the transparency is a blatant shame and the support being left in the unknown or not having the tools to properly diagnose is concerning.
Anyhow I hope someone googl'ing this might find relief in a similar situation.
TL;DR; Solution: Backup - Wipe - leave it online on factory settings for a few hours - restore backup and get a good night sleep despite the sour taste that left.
All the best