If a beginners point of view is useful, let me tell you I'm using Ear Trainer on iOS and was using Complete Ear Training on Android, I've only been doing it for like six or eight months with a break in-between. I went from nothing to being able to recognize m2, M2, m3, M3, P4 and P5 upwards and I'm working on m3/M3 downwards and harmonically now, usually with 85%/90% accuracy. I can also tell major from minor 7th chords apart with like 70% accuracy and tell the major and minor scale and their pentatonics apart upwards and downwards with above 80%. All this with different root notes, same root note is way easier.

If you are interested in transcribing I would recommend a teacher. My girlfriend can arrange live on piano and has insanely good absolute pitch and she helped me on moments of extreme confusion and frustration that I wouldn't have gotten out of on my own. Also I have a tuner app on iOS that plays a reference pitch and also tells you what interval you sang, it's called TonalEnergy Tuner. I didn't need to sing until I got into learning downwards intervals, and I think I would never would be able to learn those without being able to sing do re mi in tune. Singing for some reason really helps you "imagine" and remember tunes.

On the same amount of time I am now very seldom but sometimes able to transcribe very simple synth lead melodies to my synthesizer, as I was also learning basic sound design in parallel to this.

One year ago I didn't even know you could learn absolute pitch as an adult, I'm 37. I'm completely mind blown by the fact I learnt what I learnt so far and sometimes I just don't believe it happened and am scared it will just like completely go away or something because it's like a very alien thing for me to be able to do. I don't even know what my objective is but it's probably being able to musicalize things in my mind and being able to jam with friends.