I am having the same issue and I can consistently get the game to not save by having my daughter join the game on her switch. What's really odd about this is that last weekend we were able to play for hours one evening but after that save worked we were not able to play again at all. We did try one more game together and it didn't end up saving either so we gave up playing until this bug is resolved. I am playing on a PS5 and my daughter is on a OLED Switch.
I decided to do some additional troubleshooting with a new game this evening and I have found that (just a few minutes of testing, not hours):
If I play solo I can save just fine
If I have another PS5 join the local mulitplayer game I can save just fine
If I have the Switch join I cannot save
UPDATE
After playing for about an hour on a LAN game with two PS5's the bug happened again. Minecraft is completely unplayable at this point.
I started to have issues on Realms as well so I uninstalled and re-installed Minecraft on my PS5. After that I was able to save local games as well.