So, I've booked some of my upcoming train trips in Italy (the longer ones) on the Trenitalia app, and most of these have generated passes for the Apple Wallet. However, one journey involves a change to a regional train, and while the inter city part with a reserved seat has an Apple Wallet pass, the regional train connection does not. It does show up in the app with a QR code. So, do I just scan the QR code to validate the ticket, or how exactly does this work?

You will scan the QR code. Even though I heartily embrace new technology, the luddite in me tells me to bring paper copies of passes & other important documents as a backup plan...
Technology is great, until it doesn't work for whaterver odd reason.

Last May we had two train journeys where we had to change from the Frecciarosa train (with seat reservations) to a regional train (no seat reservations). We never had to scan our QR code. IIRC, validating the train tickets are no longer necessary. I think they are automatically validated when you board. As J62 recommends, I did bring paper copies of all of our train reservations/passes to be on the safe side.

My comments are for train tickets purchased online. Not sure if one needs to validate paper tickets that you purchase at the train station.

You don't validate electronic tickets. Paper tickets you stick in the machine and they stamp it. But your electronic can only be used for one day and time so no worries