Were you on an AA-operated flight? Did they give you access to the Club or First side, and did they explicitly say it's because of your business flight PLUS AA status (which is not the policy)?
Pre-COVID the BA lounge used to routinely turn away anyone not on a BA or QR operated flight. I'm a PRO and flying PHL-ZRH in economy next week...
Let us know if they let you in the BA lounge. I've been turned away many times, didn't even bother to try last month on our flight to FCO.