No hot water is coming in the shower anymore...

You apparently have a high tolerance for suffering
At that pace, you’ll probably soon be able to buy a season ticket for the outdoor pool to have warm water there....

Sorry, I couldn’t resist that joke...

Hope you get warm water soon... But I would start making written complaints slowly.
If it’s a rental apartment, then maybe threaten a rent reduction. The respective amount could possibly be inquired about at consumer protection (exists in almost every city).

I hope you don’t think I’m trying to fool you, but the problem is as follows

I have a hot water meter in the bathroom, next to it there is a water outlet to the bathtub (no fitting installed), a water outlet to the sink, and a shut-off valve.

As I said, I have turned the shut-off valve on and off a few times. When I open the shut-off valve, hot water flows out of the sink at normal pressure.

Problem: Not a drop comes out of the bathtub and the hot water meter doesn’t run either... So not even when the hot water at the sink is on... I have spoken to the reading company, they want to take a look at the whole thing...

I guess the problem can’t be solved by remote diagnosis, the strange thing is that the water meter doesn’t run and only one water outlet remains dry.

I hope you don't think I'm trying to fool you,

No, I rather assume the following: not only the sink but also the bathtub has a separate hot water meter - and you haven't found their shut-off valve yet. Maybe it is under the bathtub, behind an access panel?

The inspection hatch on the bathtub is glued with silicone. I don't believe anyone would turn off a shut-off valve located behind it, close the hatch, and then glue it shut. Of course, you can't know for sure.

It is also strange that the hot water meter does not register, even though hot water is running in the sink.

Maybe the plumbing company that installed everything back then (pipe network, plumbing...) can be located?

The company not, but the multi-family house has been maintained for many years by the same type of plumber. He hopefully knows more. He is also coming by this week.