I have a slightly different symptom but appears to be same root cause. We will get the message about space during game play (usually 5 - 20 minutes of playing). Message is:
"Your device is almost out of space that Minecraft can use to save worlds and settings on this device. Why not delete some old stuff you don't need so that you can keep saving new stuff"
Minecraft: 805 MB
Delete Save Data Minecraft: 2.2 GB
Delete Save Data Minecraft Users: 577 MB, 1.6 GB, 32.3 MB
I just tried deleting the user save data with 577 MB to see if it's this 2 GB limit. I'll report changes if it would help.
Same issue on Switch