So major progress!
When our IS person initially gave me the App Passwords link (https://myaccount.google.com/apppasswords) an error message came up basically saying that the feature was disabled.
On a lark, I tried it again just a few minutes ago, and surprise surprise it worked this time! The screen that came up had a place that let me set up a new App Password, which spat out a 16-character password, which I put in the phpList config.php file. Manage Bounces → Process Bounces worked after I did that…no erroring out. Now to figure out what it did, as I didn’t actually configure any “bounce rules” or anything yet…
#BabySteps