Short answer: The old tmp behavior can be restored with a one-line sysctl change:
sudo sysctl fs.protected_regular=0
fs.protected_regular was changed to be non-zero in 20.04 which limits writes to only the owner (not even group) for files in world writable directories like /tmp
A detailed write up of the option and it's change can be found here https://unix.stackexchange.com/a/503169