As I stated earlier, the issue with later versions of OS and iTunes is related to the code signing. After you found the 12.9.5 version, all you would have had to do is follow the directions in the thread provided.
Pacifist should be able to extract iTunes from the installer but Retroactive is easier to use as long as it continues to work.
EDIT: one other thing is that iTunes 12.9.5 is not in Monterey which is why it was not installed. Mojave was the last OS that contained that and it was in later versions like 10.14.6 although there is a Windows version which has the same 12.9.5 designation.