When you’re reachable every second, people stop treating your time like it’s worth anything.

Constant availability sets an expectation without anyone agreeing to it. If every message gets an instant reply, people reasonably conclude that interrupting you is free, and they will keep doing it, not out of disrespect but because you taught them the rate. The pattern is set by your response times, not by anything you say about being busy.

Leave some messages for an hour and answer them in a batch. Tell people when you are reachable rather than being reachable always. Nothing bad happens, and within a couple of weeks the incoming volume adjusts to the new rate.