What a coaching bio is actually for
A bio is read by a client who is trying to decide whether to spend an hour of their week in a room with you. The job of the writing is to make that decision easier, not to list every credential the coach has ever earned.
Most coaching bios fail in the same way. They open with where the coach trained, list the qualifications in the second sentence, and only get to the work itself in the third paragraph, if at all. By then the reader has scrolled. The bio that works puts the work first, the person second, and the credentials last.
A new client is rarely looking for proof. They are looking for a small signal that the coach has done this before, takes it seriously, and would be reasonable to spend time with. Almost everything else in a bio is a distraction from that one signal.