Did the AOL protocol (whatever the AOL app itself used for chat etc.) go over TCP/IP, or was that its own network, parallel to the internet?

Was the limitation that you couldn't use AOL from a different ISP artificial (whitelisted IP ranges, no routing to relevant addresses from the outside), or did it actually use an "internetless" protocol that you just couldn't emulate if all you had was the internet?

I vaguely remember reading somewhere that internet access was a late addition to AOL, hence the question.

AOL was it's own network, completely parallel to the internet. It didn't use TCP/IP, it used a propritary transport called P3 - heavily optimized for dialup.

They had their own dedicated client app, where each page loaded in its own window. It didn't use HTML, it used something called "Rainman". URLs weren't a thing, you accessed "channels" (pages) by entering a specific "keyword".

Later on, in 1993, they added support for Usenet (see: "Eternal September"). Then in 1994 they added support for Gopher and WWW. So you could dial into the AOL client, and then open a regular web browser. But for most home users, there was more content in the AOL walled garden, so the web was something of a curiosity at first.

So to answer your question: It wasn't an artificial limitation. AOL was designed in a way that was fundamentally alien to the way the Internet + Web evolved.

(At some point, you could connect to AOL over TCP/IP - useful if you had a broadband Internet connection but still wanted access to content on the AOL network. This was done by encapsulating P3 inside a TCP/IP header. You still had to use the AOL client software and have an AOL membership.)