Question regarding modem

[AntonReiser]

whether this could be a hardware problem? Or is that simply impossible given that everything works except for sending text messages?

You might try turning off IMS as some people have reported it being on resulted in sending SMS issues:
https://gitlab.com/mobian1/issues/-/issues/254

Note that if you use a configuration in /etc/eg25-manager/ you need to check that it matches a potentially newer version (after updates) as otherwise it can break things with eg25-manager (/usr/share/eg25-manager/ is where defaults are located).

What carrier are you with? It could be carrier specific: https://wiki.pine64.org/wiki/PinePhone_Carrier_Support
I suppose you have already tried forcing 3G?

Frustrating how it seems to work for some people, not for others, so most likely a carrier issue.

Thanks a lot!

Forcing 3G didn't help. My carrier is O2 Germany; according to the wiki and to my experience it works without problems on other pinephones.

I'm sorry, but I can't really follow the discussion at gitlab. It sounds as if it is worth a try, but what exactly do I have to do? And can I even do it after installing FOSS fimware? (That's something I am not able to revert, but that did not worry me much because it's not the cause anyway: The sending did not work with the preinstalled firmware, it did not work when i reflashed the modem and it does not work now with the FOSS firmware.)