I have absolute pitch for select instruments only. For string instruments (especially for the violin which I play) you can ask me what note was played in the middle of the night and I’ll tell you exactly what it is. I can even most likely tell you which string and which position was used to play that note. But for other instruments like the piano, I can get close, but many times I’m within one or two notes. Surprisingly for wind instruments like the trumpet I also have almost as good accuracy as for the violin. Not sure why because I hardly ever heard a trumpet growing up.
A piano (usually) has three strings per note, all slightly detuned. Perhaps that throws you off. You could try to see if your pitch perception is affected when someone plays three identical notes on a violin (although I imagine that's rather difficult, so perhaps a small ensemble is better).
