What's the latest version of iTunes for macOS 11.7?

iMac 21.5″, macOS 11.7

macOS 10.15 or later doesn’t have the iTunes application anymore, nor can it run that. This was replaced by the TV app (video), the Music app (audio), Books app (audiobooks + ebooks), and the Podcasts app. These are now bundled with the OS, and do not need nor allow separate downloads.

Theses apps have very similar functions as iTunes before, and should contain any previously used libraries when migrated.

iTunes version 1.1.6.37

That version doesn’t make sense. It has no match in the version history list.

This might help:

What happened to iTunes? - Apple Support

The latest version seems to by 12.9.5.5 on Mojave. See if it is offered through System Prefs > Software Updates, or in the Mac Apps Store's Update category.

It may not be available at all for newer macOS versions. The most recent download I can find is for v12.8 here:

Download iTunes 12.8.3 for Mac

If this does not help, please ask for guideance in the iTunes for Mac or the Music on Mac forum sections. Your issue will get many more views there than in this "hodge-podge" section that many experienced users avoid.