To get a SIM card, open a bank account, do any kind of investments, etc. you need to do a pretty extensive ID check, which involves going on a video call with an agent and holding up your passport and moving it around in all kinds of ways to show that all the reflections are there and stuff. It's pretty laborious and intrusive

Basically you must have your identity fully checked by a third party whenever you do something that can be used for terrorist reasons, which currently includes having a bank account and using a phone. Adding instant messaging in general to that list would not be surprising.

There is an entire industry in Germany and Europe in general built around supplying this service of checking people's identities.

Yes but the state should know everything.