I’ve got the same issue with my Fairphone 4 with Telekom Germany as provider.
When I put in another SIM card from a friend of mine (Drillisch, O2), LTE data connection instantly works correctly. So it doesn’t seem to be a hardware problem, but more like the combination of SIM or network provider with the phone is making problems.
I already tried switching the APN as mentioned to “internet.telekom”, also copying all the APN Data from my old phone where everything works as intended.
I went to a Telekom store and was given a new SIM card, but the problem still occurs the same way.
I did not try using the eSIM however, but that would be more like a workaround instead of a solution.
VoLTE disabled, WLAN Call disabled, roaming deactivated
automatic/manual selection of network with no difference
Internet connection via EDGE, as well as calling/sms via GSM works like it should
Manipulating the network type in the Settings Menu which can be accessed via dialing * #* #4636#* #* to “LTE only” results in no connection at all