You enter your living room and see a pool of water on the floor. Do you say “Did you spill the water?” or "Have you spilled the water?"?

I'd go with "Did you...?". I vaguely remember from school that when telling a story you start with Present Perfect and then switch to Simple Past. E.g.

• I have broken my leg
• How did that happen?
• I was running across the street and I slipped.

So. I can see the water on the floor. The kid can, too. Hence, we're already past the "Someone has spilled water on the floor" stage and I can use Simple Past.

I've tried rephrasing the question:

"Was it you?" vs "Has it been you?"

Sentence one sounds more natural in the context.

PS. Note that the past participle of "spill" is "spilt" in BE.