Time Machine won't let me use volume
Solution 1:
I'm not sure why such behavior is occurring, but splitting the drive into 2 volumes should almost definitely fix the issue (with almost no drawbacks due to how APFS splits volumes). To fix this issue, use disk utility to add another volume to the APFS container (this has the advantage that, unlike a partition, division of space flexible). Then share both of these and use one volume per computer.