Thanks Sebastian for confirming the existing software stack limitation! The upstream Debian bug according to their Wiki, appears to be tracked under NetworkManager bug #958, and under mmsd-tng bug #5. Logs can be viewed with:
sudo journalctl --since today | grep -i mms
Workaround in the meantime is manually switch Mobile Network APN when Chatty says it has difficulty processing an incoming MMS, or before replying with media or to a group chat… which they confirm on the Debian wiki as well.