Does it have to do something on the console or on the router?

Here is a picture of the connection (fortnite):

After that I can no longer move and am kicked out of all of fortnite and then have no more Wi-Fi. After a few minutes it is there

It is probably because you are connecting to the router via Wi-Fi. W-Lan is never a really stable connection, at least with desktop PCs.

The picture only says that you have no more internet (disconnection). The reason for this breakdown can't be identified, but if you write something about Wi-Fi, 90% of the time it is the cause. If you have a desktop PC use a LAN cable.

Your ping is good. You have no packet loss, that's good too. Will be on the router. Maybe restart the router. If that doesn't help, try another game. If it is there, it will be due to the ps4

I have a LAN cable on my Xbox

Well, I have an Xbox xD and it's been like that for a year

In the second picture you can see the W-Lan LED shining, "only" the ONLINE LED is gone. This points to a different error pattern.

Is the Speedport router rented? If you call Telekom that you have lost the connection (telephoning shouldn't work then either. They can then test your line if necessary or send a new router if necessary.

Hmm then I would do a speed test two or three times in a row to see whether your Wi-Fi is constantly arriving. Sorry I don't have an Xbox so I don't know if it's possible MonkaS But you can try it. Otherwise maybe even reset the console. And is that also the case in other games?