I am a professional musician (bassoon player in a symphony orchestra). I can, if I practice it a couple of times a week, achieve and sustain perfect pitch. I had no semblance of perfect pitch until I decided to practice it at age 24. Before that the only chance I had to guess a note was to put in in relation to my own voice. Even though I don't practice this anymore (it isn't very useful), I still often just instinct…
But what I'm actually doing is remembering the pitch with the help of the timbre of the guitar string (or harp string, for my wife's harp - I hear if a string is "off" even if it's the first single note I hear in the morning). I believe I would quickly be bewildered if I heard pure sine tones. And that's it. There's nothing more which is even close to what people with absolute pitch can do. I haven't run into that many of them, but it's like they see all the music in color, it's a different world (and they are often constantly bothered by out-of-tune sounds from life). Hit some random notes in parallel and they can tell you the notes instantly. And so on and so forth.
The other thing is what happens if they lose the perfect pitch.. which does happen, with age, for many, or at least it de-tunes a bit (drops a semitone, for example). Then, when it's gone, they don't even have relative pitch to rely on. Rick Beato interviewed a couple of people this happened to. I don't want to be there. My little ability to tune without a tuner is enough for me, and what it is is trained pitch memory - not absolute pitch. And it's relatively common, unlike absolute pitch.