I really enjoyed it, especially Cathedral level, but I feel like

Thief is one of those games that does story right.
There's a good story if you care, and take the time to read it and enjoy all the world building.
But if you're just "tl;dr fuck this gay shit" the story is basic enough that it frames for an excellent game.

So I wouldn't be too worried about missing the story if it ain't your thing.

It has a very good story, OP.
Replay the game, watch the cutscenes and try to read everything. There are some plot-related easter eggs early in the game.