how to uninstall completely Adobe from Mac and install again

Have you contacted Adobe about full removal of their product? Any other uninstaller from a non-Adobe source may miss part of the Adobe installation, or take parts of other needed products with it.

Perhaps the relevant Adobe application forum will point you to an Adobe authorized full uninstaller for the product. If you upgraded to Monterey from an older operating system that supported the Adobe CS5/6 products, then it raises a question if any uninstaller exists, or if it is 64-bit, so it might run on Monterey.

Find Any File...

http://apps.tempel.org/FindAnyFile/index.php

Hold Option or alt key when selecting Find to Find All.

Find All for... Name>contains>adobe