I've heard people say that powerful magisters and sorcerors live longer than usual.

But, that got me wondering: would all magical ability naturally increase lifespan, or just Restoration or something?

Any magical aptitude will extend your life. But, when you get to 1000 years old, perfecting other branches is just second nature. Only dumb asses from the Mages Guild adhere and only study the separate schools as if they're not interconnected.

There's a reason why Psijjics, the Telvanni magelords, and Dyviath Fyr are nearly as old as recorded history, something even most of the altmer are super insanely jealous of.

I seem to remember an elf in Redguard, talking about how almost all human mages eventually turn to necromancy to extend their lives as they get older and start to fear their deaths. Of course, that was probably just elven conjecture toward humans. That was also substantially longer ago in time, then the TES main series.