An update, I did email support on this and they had be produce and send logs from ModemManager. Here is a quote from one of the developers:
One thing I see in the logs are “Transfer Route MT” messages. When I get one of those from my carrier I don’t see any more SMSes until that message gets ACKed.
According to Purism these occur with MMS and VoiceMails. They suggested that I put my SIM card into an Android phone to free up the messages. By the time I got that suggestion, I had already done that and all my delayed messages came into the Android phone. When I put my SIM in the Android phone I also got my APN settings updated so I wrote those down. The only one I could put in the Libream phone was the name and apn value which I added since they weren’t there already. With my SIM card back in the Librem 5 I could again get messages.
FYI, the ModemManager issue that discusses issues with ModemManager properly handling MMS messages is issue 257