Why can't I delete old Time Machine backups?

Don't use CMM, old TM backups should only be donr in TM itself.

Deleting Backup Files from Time Machine E… - Apple Community

Use Time Machine

You can use the Time Machine application itself to remove old backups; here’s how:

• With your external storage device connected, open the Time Machine application from Launchpad.
• Locate a backup for removal, then select it.
• Click the gear and select Delete Backup.
• You’ll need to confirm your password to complete the removal.

Thanks very much for this. So if it's normal for the Time Machine disk to become full, do I just leave it and let the back ups continue to collect on it?

Yes, as long as this will work for you. Here, I am assuming that the Time Machine backups are on a Time Capsule.......correct?

But.....at some point, you are going to see a notice that Time Machine cannot delete enough old backups to make room for the new backup. This usually happens after an operating system update or you have added a lot of new data like photos, videos, music, etc to the Mac.

If the Time Machine backups are stored on a Time Capsule, my suggestion would be to connect a USB drive to the back of the Time Capsule and use the Archive function in AirPort Utility to copy all of the data on the Time Capsule drive over to the USB drive........in case you need to go back and retrieve data from an older backup.

Then, erase the Time Capsule drive and start over again with new backups.

If you don't have a Time Capsule, then apologies for using up a few minutes of your time.

Do NOT attempt to delete things directly from a Time Machine backup volume.

If you've dragged files from the Time Machine drive to the Trash you have 2 options:

1 - return the files to the exact location of the TM drive if you can.

2 - if you can't, you'll have to erase the drive, reformat APFS and start over with a new backup (which will be full and take some time to complete).

This will include CleanMyMac , aka “ BrickMyMac “

As the aka name denotes

Start Over from Scratch

For Intel computer >> Use Disk Utility to erase an Intel-based Mac followed by How to reinstall macOS

Thereafter to start from scratch and install all Required Applications directly from the Apple Apps Store or Directly from the Developer.

If going this route - I suggest Not using Startup Assist to migrate things back as this will probably Re-Introduce the existing  issue ( BrickMyMac ) at the time TM Backup was made 

You don't need the Seagate software so it should all be uninstalled according to the developer's instructions.

That feature has been removed.

As others have already stated, "CleanMyMac" is the problem. It is attempting to get you to do something that is certain to corrupt your backups, making them useless. Time Machine disks becoming full is normal. Leave it alone.

Be prepared for the necessity to erase that Mac. That's how bad it is. Rule 1 of Macs is don't install junk.

How much free space is on both drives?

Are you running any VPN, Anti-Virus, or Cleaning apps?

Get rid of CleanMyMac. It’s complete garbage. It will do more harm than good. As long as you have it installed, any further troubleshooting is pointless.

Yes.