What ways are there to automate installation of a list of apps?
“adb install” can be used to install apks without rooting the phone.
fdroidcl can automate downloading apks from F-Droid.
Is there anything similar that can install a list of Play store apps / package names?
Not really. I’m sure you could set something up using fdroidcl or eget or something to grab apk’s from Github, but nothing would be “automated.”