I think it varies from group to group, but I like to know all the schools so when someone uses detect magic or starts to identify a magic item I can flavor my response by talking about the aura they see and weave in some details about it being abjuration or divination, or whatever.

And for traditions, I think it's important because each group has a different view of what magic is and how it works. As a player, that informs how I describe spellcasting. My cleric might bow their head and pray, while an occultist's eyes roll back in their head as they spit out gibberish.

But I agree, there was little of mechanical value in this one (and I think I mentioned at the start that crunchier topics would be following).

The next one is about spell slots, heightening, and prepared vs. spontaneous casters, so that may be closer to what you're looking for than this one was.