So it looks like the Reset this PC feature worked because I didn't do the cleanup after unchecking the Recovery Reset support compatibility and activating DISM ResetBase Functionality.
Exactly.
What if I uncheck the System Reset compatibility and leave the DISM ResetBase Functionality disabled? Will I be able to use the Reset this PC feature even if before doing it I use the Dism /Cleanup-Image /StartComponentCleanup /ResetBase command?
Yes, but look at each component with which compatibility it is locked and do not remove those that are locked by System Reset compatibility.
What about the clean update backup option of NTLite?
The DISM option is a free feature you can use to cleanup. It is equivalent to the command with Dism so this name.
This will remove the old files that have been replaced by the new files contained in the updates.