Some time ago me and a friend were able to play with each other through the Local Network feature in Trackmania 2020.
I created a server using Standard Access, he joined using Starter. Has there been any update that changed this? Going through the patch notes I didn't notice anything that talked about this, and now it's not possible for him to join, since Local Network asks him for Standard Access. Is it a bug or intended?

It should still be possible. If it's not, it's probably a bug.

You should submit a report to the game devs on their forum:
Ubisoft Discussions - Trackmania - Player Support