If this is actually a 7th-generation iPod nano, rather than the iPod touch listed under your post, I wouldn’t downgrade iTunes yet.
Apple still documents using iTunes on Windows 10 or later to sync an iPod nano, classic, or shuffle, so an older iTunes version shouldn’t normally be necessary.
Before uninstalling anything, I’d first check whether the nano appears in iTunes when you connect it. If it does, what happens when you try to sync music — do you get an error message, or does the sync simply not start?
Apple’s current syncing instructions are here:
Intro to syncing in iTunes on PC - Apple Support
I’d identify the actual sync problem first rather than risk creating an iTunes library compatibility issue by installing an older version.