the difference between a ROM and a mobile OS, since I use both interchangeably (colloquially speaking).

Most people mistakenly do. GrapheneOS much prefers people to use the proper term of OS, so I try and do so.

I didn’t know about play integrity. Is this new with Android 14?

Nope. PlayIntegrity was announced anout 2.5 years ago. SafetyNet actually sunsets 31 Jan 24, unless the dev got an approved extension, and then it’s 31 Jan 25 for that specific app.