iTunes supports some pretty damn old devices (as the most recent version works with the og ipod). I doubt you’ll get a answer faster than just trying to hunt and download old versions of iTunes on your own computer. Finding old iTunes software that runs on Mac is really really hard, but I don’t think your going to find somebody using a 1.0 device that can just answer your question of what works. I’d research the version 2-3 years ago, try to find that and work back from it.
The fact that a current Mac (M1) with iTunes through finder can still connect to an OG iPod running OG software through many dongles however suggest the problem is very likely on your touch‘s end and not on the Mac. Ie the device might be fried from disuse, most old old devices still connecting and working have been used constantly and upkept through their life.
You can give Windows a shot since it can install very old version of iTunes without problem.
I would install a old OS in a VM.
Thanks for the suggestions. Rather than trying to deduce the most recent compatible version of iTunes, I figured I'd try looking for the oldest compatible version of iOS.
So I dug out my 2006 MacBook that has a Windows XP Boot Camp partition, and used iTunes 7.5 to try out iOS 1.1.1, 1.1.2, 1.1.3, 1.1.4 and 1.1.5.
Unfortunately, none of those would sync with the latest version of iTunes on my Mac mini running Mojave, or the Big Sur Finder on a MacBook Pro.
So then I found the original iOS 3.1.3 IPSW I downloaded back in 2010. This time I couldn't install it using iTunes 7.5 in Windows but I could using iTunes 8.2 in Snow Leopard, and now the iPod touch appears just fine in both iTunes and the Finder.
(Upgrading from 1.1.0 through 1.1.5 was as simple as holding down Shift while clicking Restore, but both installing 3.1.3 and downgrading back to 1.1.0 did require restarting in DFU mode.)
For now I'll leave it on 3.1.3, so that I can use my current iTunes library, but when I fancy using that even-older-interface I'll DFU-restore to iOS 1.1.0, it's much much faster to do so than current versions of iOS.