Would you buy a new Thief game if it was a proper sequel with large levels and fun gameplay/story?

Absolutely, if it was any good.

Thief is ideally suited for sandbox, but ultimately focused, level design. I don't think it should be an "open-world" design like Assassin's Creed or whatever. But entire chunks of a city or specific area would be good, with branching paths and multiple ways to approach the mission.

I'd also like to see the concept of verticality further explored, as I think many games don't really make use of tall buildings and Thief really could. I think it would match the lore well, too, as the games seem to jump forward from bronze-age primitive stuff to more industrial steam-punk concepts...it wouldn't be crazy to see the advent of multi-leveled skyscrapers in a newer game, rife with all kinds of opportunities to infiltrate, steal, and explore.

I certainly don’t see why not.

Yes. Both the IP and genre have much more to give.

But I don't think any studio wants to touch the IP. Since stealth games are not popular, making one in an IP no one under 30 would buy is probably a bad idea.