I had even bigger system data - around 620GB on a 1TB disk.
No way to shrink it. I then managed to shrink it by shutting down the Mac, booting into recovery, starting a terminal and disabling file system integrity protection:
csrutil enable --without fs
After a reboot, it kept shrinking and within minutes, the system data shrank to around 60GB.
Another shutdown, recovery, terminal and
csrutil enable
to re-enable file system integrity protection. Let's see if it will grow again.
Looks like the whole file system integrity protection is full of bugs. I had the issue that after a new install and a full restore of my time machine backup, the /Application folder was write protected so I couldn't install apps or updates any more. Apple support told me to erase my Macbook Pro 16 M1, re-install Monteray, use TM restore but without the Apps and then manually re-install all the apps.