First, you need to reformat the backup disk to use HFS+. Time Machine does not work properly on APFS volumes. Second, please go to the View dropdown menu in the upper left of Disk Utility and select Show all Devices. I need to see what is shown for the Other Volumes on both disks. Third, which disk is the backup disk. Fourth, have you created more than one volume on each disk? Fifth, for the boot disk, select the volume shown under the Container in the Show all Devices listing.
Time Machine is an accumulated backup model. That means after the first backup, Time Machine makes incremental backups that are added to the backup disk. That is why Time Machine can "go back in time" and restore earlier copies of the same file because it keeps all versions after any changes made to the file. Hence, over time the hourly backups accumulate and use more space on the backup disk. Although, Time Machine will delete backups, it does so when the backup disk is running low on space. Time Machine continues this process until the next backup requires more space than Time Machine can provide. At this point you receive an error that the disk is full. Either you can replace the backup disk with a new one or erase the backup disk and start over. Thus, if you have a 1TB backup disk for a 1TB startup disk, then the backup disk is not large enough. It should be at least 2-3 times larger than the disk Time Machine is backing up. In your case, the backup disk should be a 3TB disk to backup the 1TB startup disk. This will provide sufficient backup space so you won't have to start over in just a few days or weeks.
When you configure Time Machine, you should exclude certain things such as a Parallels emulation disk because even if only one byte changes on the Windows "virtual disk", Time Machine will backup the entire 20 or 30GB virtual disk. This eats up all that space on the backup disk for even minor changes. If you don't need to have a full system backup, then you can exclude system files. However, if you do that, then you cannot restore a bootable backup. You can restore all of your file but you must re-install macOS first.
Here's a short explanation of how Time Machine works, and it's impact of what happens when a backup disk is full.
Time Machine deletes older files, if they have been deleted from the source, when it needs space on the backup drive for a new incremental backup. Time Machine "thins" it's backups; hourly backups over 24 hours old, except the first of the day; those "daily" backups over 30 days old, except the first of the week. The weeklies are kept as long as there's room.
How long a backup file remains depends on how long it was on your Mac before you deleted it, assuming you do at least one backup per day. If it was there for at least 24 hours, it will be kept for at least a month. If it was there for at least a week, it will be kept as long as there's room. By default, Time Machine backs up hourly. That cannot be changed in Time Machine. There are third-party utilities that will modify the backup interval such as Time Machine Editor.
The Time Capsule's sparsebundle grows in size as needed, but doesn't shrink. Thus, from the user's viewpoint of the Time Capsule, it appears that no space has been freed, although there may be space in the sparsebundle.
Once Time Machine finds it cannot free up enough space for a new backup it reports the disk is full. You can either erase the backup drive and start over or get a larger drive.
