I am respected by everyone around me.

Nobody announces this. It shows up as who gets asked — whose name comes up when something delicate needs handling, who is told the truth about a problem rather than the tidy version, whose objection makes a room pause.

Those are the actual signs, and they run quietly enough that a person can be widely respected and entirely unaware of it, especially if they were waiting for an announcement.

Some of what lands on your desk didn't have to land there. Someone chose you over the alternatives and never explained why, which is what this mostly looks like in practice.