Follow On
As the TM Backup was set to Manual and was left " after some months have passed since the first one. " this would tend to indicate that all the Personal Data is not too important to the User.
Further, leaving ones Important and Non Replaceable Personal Data unprotected is generally not a good idea.
Predicated on the above - you can use Erase and reformat a storage device in Disk Utility on Mac - Apple Support (CA) and Start a New Time Machine Backup Regime from Scratch
Understand - reformatting the Entire External Drive will remove ALL Data from the drive and can not be retrieved under normal circumstance
As for " CleanMyMac " have been installed and used on this computer >>
Specific to CleanMyMac aka “ BrickMyMac “
The steps in #1 below is predicated on the Offending Application has been Removed as per the Developers Specific Instruction
#1 - Some Contributors suggest restarting in Recovery Mode and choosing to Reinstall the Operating System over the existing installation.
This may or may not replace elements of the Entire Operating System including the Home Folder ( User Account ) and replace any corrupted or removed elements of the Operating System and make thing right.
#2 - Then there are Other Contributors ( like myself ) would suggest from this link Use Disk Utility to erase a Mac with Apple silicon.
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 Application 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 that existed when the TM Backup was made as this will probably Re-Introduce the existing issue that existed when the TM Backup was made