I think the whole stack of operating systems and tools that assume that this is possible get in trouble when it's not possible. I don't want my computer to become a locked down sandbox but it seems like this is where we are headed.
The only solution is to copy all the files you want to keep to another (not full) disk, then reformat and copy them back, or if you don't have another disk to copy to, somehow edit the disk directly to "manually" free some space.
It's true that mounting the affected Data partition on another machine won't help.
And booting Recovery and mounting is equivalent to mounting on another machine.
But it can help, as follows.
Before resorting to a wipe, try booting into Recovery, mount the Data partition, then use rm on a large file. When it fails, unmount the Data partition and run fsck -y on the Data partition at the commandline. If it finds errors and fixes, you'll get free space.
If you can't figure out how to mount the Data partition read/write at the commandline, close Terminal and run Disk Utility, locate the "Data" partition in the sidebar and right-click to Mount. Quit Disk Utility and restart Terminal. You will find user's data files the /Users folder.
You can locate large files on the mounted Data partition with find /Users -size +100M
Use df -h /Users to verify that 100M or more are free. Find and rm large files as needed. Then boot normally and finish cleanup from comfort of normal operation.
Note— Running fsck via Disk First Aid in Disk Utility should be the same as running fsck -y at commandline, but the UI for Disk Utility can be confusing. For example if it can't unmount the drive to perform the repair, DU will misleadingly advise you that the drive has failed and cannot be repaired. DU has some other odd behaviors, so it's more effective to use fsck at the commandline.
Another fine point: It's the specific APFS "Data" partition filesystem that's locked up (user's data), so you need to repair that specific volume, e.g. disk2s2. Look up the Data partition with disutil list Repairing the drive as a whole (e.g., disk2) is not what you want; this just checks that there's a partition table, which will naturally be OK. Similarly, repairing the other APFS system partitions will not help, nor will repairing the APFS Container disk. Fix the specific "Data" partition.