Love the idea that Gordan has known Bruce’s identity for years now because he is a detective afterall and arguably you don’t need to be as good as Batman to figure it out. So he’s just known and kept it to himself and he pretends for Bruce’s sake. I don’t think Gordon is an esp good actor but he’s very good at evading things he doesn’t know how to approach. When Bruce does finally reveal himself Gordon’s lack of reaction is suspicious and the truth comes out.
(this is based off 2022 Batman but can be applicable other places) Going along with this thought I also really like when Gordan and Bruce are friends simply because they’ve worked together for so long, and indirectly Bruce has let him in on a part of his life only his immediate family sees (that part being Batman). While in costume Bruce can hide most of his humanity but there’s always going to be small things that can’t be hidden. Gordon has seen him investigating enough to know his patterns and see beyond the cowl (metaphorically). Esp when Bruce was first starting out, Gordon is already a fairly seasoned detective and it only took a few investigations for him to pick up that this guy was young and that was the first time Gordan truly saw Bruce as human.
Neither would realize they were actually friends until embarrassingly late. It would take like a throw away comment from Dick.