I'm currently using the one directly from Apple. I'm reluctant to try this unless you're sure that it won't do anything silly like erase all my backups, clean all my non iTunes media (imported CDs, stuff like that) off my phone, etc. (When I changed PCs, pretty much exactly that happened, so it's not a theoretical concern.)
The thing is, this is one of those slightly annoying things that niggles at me rather than being truly annoying, and there's a trivial way to "work around" the problem - start iTunes manually - so I'm not really up for messing up my phone's set-up. It's also really hard to search for posts on forums (any forums) from people having the same problems. Two thirds of what Google finds are people who want to *stop* iTunes from automatically starting (and they say to turn off the option that I don't have), and most of the rest are people whose PCs don't even realise that the iPhone is an iPhone even when iTunes is launched manually, which mine *does* realise.
However, I just tried a different search (itunes no option to launch automatically), and found this thread on these forums: iTunes Not Opening - Apple Community
So it's not just me, and nobody really knows what causes it or how to fix it. User "Goose_85" had (before posting) even tried twice with the Apple-website version and twice with the Microsoft Store version, with the same result on all.