The rule for games is that you have 16ms (for a 60Hz monitor) to process all input and draw the next frame. That's a decent rule for everything related to user input. And since there are high refresh-rate monitors, and it's a web app and not a game using 100% CPU & GPU, just assume 4-5ms for a nicer number. If you take longer than that to respond to user input on your lowest-capability supported configuration, you've got a bug.

0ms is great, 4ms is very good, 16ms is minimally acceptable, 20ms needs improvement (you're skipping frames), 200ms is bad (it's visible!), 500ms is ridiculous and should have been showing a progress bar or something.

Responding to input doesn't necessarily mean being done with processing, it just means showing a response.