"For me the pitch assessment accuracy differs depending on the harmonic content of the sound: guitars and harmonicas are awful, but pianos and flutes etc. seem to do better."
It is common for musicians with relative pitch skills to be better at it with their own instrument(s) than others. For example, I hear guitar parts better than most other instruments, and I've played guitar for three decades. I can do pitch recognition with other sounds, but the further from the range and timbre of guitar it gets the trickier it becomes.
I think absolute pitch is fascinating and confusing...because pitch is arbitrary. We've all mostly agreed on A=440Hz, and it's become more common with time and electronic instruments and tuners and such for recordings and live performances to be A=440Hz. But, I still find myself retuning sometimes when learning new pieces by ear, because the recording is a little sharp or flat. And, it's arbitrary that we have 12 notes to an octave; we could have 17 or whatever (based on closely matching the ratios, so it's not completely arbitrary).
So, absolute pitch is clearly a learned skill. The wild thing about it is that it is a learned skill that is mostly only obtainable when very young. This is similar to some language nuances and why someone may speak a second language with an accent even after decades of speaking it fluently, if they learned it as an adult. There aren't a lot of skills like that, however...I can't think of any others, and it seems to be because pitch/music/language are all closely related in the brain.
I wonder if in your case, you could retune your absolute pitch with practice? Perhaps you don't play or listen to as much music as you did in your youth when it was "in tune".