My wife and I both have Note 10+ phones and are both experiencing the same issue. With the stock messaging app If either of us are on Wifi we cannot send or receive mms to each other. We can send Mms on wifi to any phone not using the stock Samsung messages App. So if I Switch to Android messages we can then both send and recieve mms to each other with Wifi on. So it is only Samsung messages to Samsung messages that won't send or recieve mms when wifi is on. We both have wifi calling off and advanced messaging on and are on the At&t network. Before our Note 10+'s, she had an 8+ and I a Note 8 and we did not have this issue. Any ideas how to fix this issue as we both enjoy using the stock messaging app on our phones.
Have you attempted to force stop and clear cache on the messaging app?
Navigate to your settings > apps > find and click on Messages > force stop > storage > clear cache.
Also, Have you confirmed both devices are currently up to date?