when I purchase Clean My Mac X after I put my password I faced this message

Part 1 of 2

Any Third Party Applications that will interfere with the normal operation of the OS,  is an invitation for disaster. 

Certain Applications maybe available on the Apple Apps Store - this only means the Developer is prepared to pay Apple a portion on each sale. What the Application may do to the computer is up to the User to check this out before purchase

Any of the below should be removed as per ➡️ Developers Instructions ⬅️

1 - Disk Cleaner 

This will include CleanMyMac , aka “ BrickMyMac “

Read some of the posting and arrive at your own conclusions.

Part 2 of 2

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 

so how can I uninstall the programs with a perfect way?

If you used an installer, then use the uninstaller provided by the developer.

If it is an App Store app or Drag and Drop into Applications from a disk image, just drag it to the trash.

Take this as a sign from above.

CleanMyMac is garbage. You absolutely do NOT want it on your Mac.