When the iPhone 14 family shipped, with iOS 16, their Technical Specifications said that syncing would work using El Capitan 10.11.6 and iTunes 12.8 or later. Now, with the iPhone 15 family, the minimum requirement is High Sierra 10.13 and iTunes 12.9 or later.
Someone said in another thread that the syncing requirements are really tied to the version of iOS instead of to the iPhone model. If that's true, then it's a safe bet that once you upgrade your iPhone 13 mini to iOS 17, you won't be able to sync it with a Mac running El Capitan any more.
That still leaves the question of why syncing an iPhone running an iOS 16.4 did not work.