It's discretionary. I'd want at least an inch, but 2 probably wouldn't look bad.

I think you you can go from 1" minimum to 2" max depending on your preference . I have 1.5" . You need the overhang so that if there is water dripping from the tub , it won't come on the wood panel .

We're doing a slab on the side and on the top. The tub will be undermounted.

What's the minimum overhang to hid the seam where the two pieces join together? Will 1/2" look right?

Can you do a mock up with a couple boards? In a small bathroom you'd always be looking down on it so you only need enough to keep drips from running down the outside of the tub. Instead those drips will hit the bathmat or rug you have there, right? If you'll be looking at it while sitting on the toilet across the room, or while lying in bed in the next room you might see the caulked seam unless you have more overhang. I'd go with more rather than less.

-Babka

Overhang will not prevent drips from running down the edge, back across the overhang and down the front of the tub/cabinet.

If you're worried about this, have your fabricator cut a 1/8"x1/8" drip slot on the underside of the granite just behind the edge profile. The water can't jump the slot and will hit the floor instead.