Ok, I solved the mystery. For the desparate future reader, here's the essence: Stay away from ebay spare parts!
Prior to this ordeal, I changed the USB-C board because USB data didn't work, only charging. The USB worked fine again with the replacement board, so I didn't think it was related to the issue. The reception was always bad at this location as reported by the owner (it's not my phone, so I couldn't judge whether it became much worse after the port change), but I noticed that weird 2G issue while 4G seemed to work normally (just bad reception at the location). The spare part from ebay had the correct part number for the region-specific model printed on the PCB, exactly the same one as on the original PCB (SM-G981B), only some components and the printed text font looked a little different, maybe a different revision, no big deal, right? Wrong! Although USB worked fine again with the new port, under closer inspection, there were some tiny components (capacitors or filters) missing compared to the original board next to what I assume is an antenna pre-amp IC. Putting back the original USB-C board restored the 2G functionality, so the GSM fallback works again!
The irony is: Turns out, the original USB-C port wasn't even broken, just full of compacted black lint and fluff and whatnot, which apparently prevented the USB plug to go in all the way to make contact with the data pins, but the power pins are a little bit longer which was just enough to make contact. After proper cleaning, the original USB-C port works again, so I put the original board back and called it a fix. Thanks, knock-off ebay sellers, for saving 0.07 cents on SMD components to render a $10 part useless.