Time machine is supposed to be clever enough to delete the oldest backups to make room for new ones.
That's the theory. In practice, things don't work all that well when the Time Capsule is close to being full and a new backup is a bit larger than normal. Then, Time Machine cannot delete enough old backups to make room for the new backup. Of course, Apple does not tell you about small details like this.
When this occurs, you have two options:
1) Connect a USB drive to the USB port on the Time Capsule and copy or "archive" all of the data on the Time Capsule drive over to the USB drive. Then, erase the Time Capsule drive and start over again with new backups of your Macs.
2) If you don't really need all the old backups from many weeks, months and even years going back in time......(few of us ever do)......erase the Time Capsule drive and start over again with new backups of each Mac.
I've been told that if you try to backup two or more mac devices to a single partition it can't decide which old backups to delete, so it remains full and the new backups fail.
You got incorrect information. Time Machine will try to delete the oldest backups of the Mac that is currently trying to back up.
I'm also not convinced that all, or any of the backups are accessible. Most of the backup dates/times indicated in the right hand side bar when entering Time Machine are greyed out.
If you are using WiFi to connect the Mac to the Time Capsule, it might take 15-20 minutes or more for all of the old backups to fully load. Sometimes, Time Machine will perform a check on the integrity of the backups before they display. This will take even longer.
When I've changed the backup device to an external hard drive it produces folders for each day and the full backup folder tree is accessible directly.
That is because Time Machine backs up differently to a "network drive" like the Time Capsule than it does to a "local drive"......one that is connected directly to a Mac. Time Machine backs up to a special type of file called a "sparsebundle" on a Time Capsule. If you are running the Catalina operating system, Time Machine backs up to a similar type of file called a "backupbundle".
Time Machine backs up to normal looking folder called "Backups.backupdb" on a local drive connected directly to a Mac.
You can see the same type of folder layout in the Time Machine backups of a Mac on the Time Capsule, but it takes some additional steps to drill down through some layers before the dated folders will appear. If you are curious, we can provide the steps to do this, but it won't help the current issue of not enough free space on the Time Capsule drive.
However, it's not obvious how to partition the disk in Time Capsule. It doesn't seem to appear in Disk Utility. Is this possible?
The only way to partition the disk on a Time Capsule is physically remove the drive from the Time Capsule, place it in a caddy or enclosure and then connect that device directly to your Mac. Not an easy task, even for a technician. But, even if you do this, you will still face the issue of the Time Capsule running out of space at some point with not enough space for new backups. Nature of the beast, I am afraid.