What version of iTunes is required to upgrade a phone to the current version of iOS 13?

I have a Mac running Sierra with legacy iTunes 12.6.5.3 and an iPhone SE on iOS 10.3.3. I would like to upgrade my iPhone to the most recent version of iOS 13 via iTunes. When I connect my phone to iTunes, it does show the iOS 13.3.1 update available to download and install, however I have found online someone saying that this isn't really compatible and will put the phone into recovery mode.

Running legacy iTunes, I no longer get updates to it in the app store, but I found iTunes 12.8.2 available from Apple's page at https://support.apple.com/downloads/itunes dating back to February 2019. I could not find clear information about whether this was compatible with iOS 13, if it would work to install it properly, if it would recognize it after installing. Or, was the information online mistaken and iTunes 12.6.5.3 will also work? Or, is there a more recent version of iTunes for macOS Sierra? Or, is it impossible to use macOS Sierra to upgrade a device to iOS 13?