When I was teaching bass lessons, I'd often have friends, usually also in their mid-20s ask me, "Could I still start learning to play an instrument?"
My answer was, "Yes, but you probably won't be any good. Not because you're too old to learn, but because if you had the right inclination to be good, you'd have already found your way to an instrument." (This is totally different from learning additional instruments later in life.)
Learning to play an instrument creatively (as is your stated goal) is a long process of learning to build up intuition both about the structure of music and the way your instrument works, both mechanically and harmonically. Most of that happens in your head, not in your hands. There are methods that may be more or less efficient, but they all require years of effort.
That said, playing an instrument is fun. Learning to play a few songs on the guitar or piano is a totally attainable goal for a few months of effort. Really, something equivalent to that (including, e.g. middle school band class) is where most people get started. That remains fun even if you don't get to the point that you're using the instrument as a creative outlet.
I started piano when I was 23/24 with the goal of wanting to play Jazz / improvise and quickly realized that the biggest challenge is lacking the technical skills to translate the "mental orchestra" onto the keys.
Especially before bed my mind wanders and produces these amazing Blues/Jazz riffs or Moonlight Sonata-esque ideas, but my talent is far behind my taste when it comes to either trying to play or even transcribing all that I "hear"... at least without significant manual effort.
So yeah, maybe that just confirms what you're saying, but what I realized around year 1 was that "improvisation" is really just a musician's bag of technical skills/tricks combined together in their own unique ways... And ultimately the more technical capability you have, the more "improv" things will appear.
That doesn't mean that composing becomes automatic -- often once you cross that chasm, there's still frustration between having an abstract musical idea, and translating it into actual notes. Also, by that time, the way you listen to music has changed pretty drastically, and you also realize that a lot of your own ideas are mundane in comparison to the things you can half-way understand in music that you listen to. That's where most of the work actually happens -- in becoming better at thinking about musical ideas.
If you're able to sing the ideas that you've got, I'd recommend recording yourself singing them, and then spending the time learning to play those ideas. That at least lets you work on the gap that you mentioned between thought and mechanics in a concrete way.
For most instrumentalists though, myself included, you pretty quickly get to where you can play things more easily than you can sing them. If you ask a trumpeter to sight-sing a piece of music, you'll usually see them miming the hand movements because they can imagine how it will sound when they play something, and work backwards from there to singing.
I just started his Blues Bible course[1]. Maybe that could help speed you up. It's tons of riffs to help get you improvising. But yeah, he says riffs are basically just a bag of tricks you can dip into.
[1] https://pianowithjonny.com/products/bible-of-blues-riffs-vol...
Double down on ear-training, it'll take you a long way toward being able to being able to automatically translate the imaginary sounds into real play.
1) Think about the music you enjoy listening to the most and what instruments are most prominent in it. That's the instrument you should choose. Like getting good at anything else, practicing music is hard and can be chore at times. You won't always have the inspiration to play. The best way to consistently practice and improve is to be learning song that you really want to be able to play.
2) Playing with others is absolutely essential. You will improve more jamming with others for an hour than you will in ten hours of practice on your own. You do need some amount of skill to do this, but not an awful lot. Once you have a little bit of confidence built up, look for others at a similar skill level to meet once a week or so and play together. You don't need to form a band or anything, but you just might find that you want to.
3) Music theory is nice to know, but not essential at first. It is very useful when writing music of your own and improvising with others, but there's a bunch to nail down first before not knowing it will hurt you at all. Learn basic notes and chords, then focus on picking songs you want to know and learn to play them well. While learning songs, think about what music theory you have learned and how it works within the song.
4) The truth is that becoming "good" will take a decade of dedicated work. But if it is something you truly enjoy then after a year or so you will be able to get to the point where it is both fun and very rewarding. So really do focus on your enjoyment of it. You don't have a parent requiring you to practice for an hour a day anymore, and you won't find immediate benefit from it at the start. Anything you can do to make it an enjoyable routine is very very important. I won't recommend specific books or methods because you fall into the same problem as telling someone how to learn programming. There are so many different options, but what's important is to find what you like the best.
Absolutely.
There's no point picking up the guitar if you don't listen to any guitar music.
Having said that... As with learning all things... It's definitely more enjoyable when you progress quickly.
Someone met a world-class concert musician after a show and said "That was incredible. I'd give my whole life to play like you," and she replied "Well, I did."
The ways of producing good sound and good tone are still dark arts with wildly conflicting opinions on them. To me it seems the good players already had a sense of what to do right and then built on that with tons of practice. You might end up going down a dead end with your practice and no one can really set you right because they 'just got it'.
A good private tutor if your other option.