The problem I stated above regarding my data connection Is a problem other users of the 10 III device have, too. It has nothing to do with APN settings (see: Unable to use mobile data on Sony Xperia 10 III 4.4.0.64 for more details)
I re-installed android 109 on the device, erased/wiped everything and then did a fresh install of Sailfish OS. No problem since. So hopefully this was just a “glitch”.
Thank you all for your time!