Welcome onboard RodionGork! You are in the right place. I'm also new here and within only few months I've gotten so much knowledge and warm help that you probably won't get from any other forum on the internet.
Since you live in Russia, in my opinion you should at least try a bayan (which in Russia specifically refers to a B-system chromatic button accordion with free bass system) for several reasons:
First of all, your piano skill won't give you too many advantages in learning accordion actually since you need at least 3 different skills combined together to play an accordion/bayan:
Not to mention the other aspects of accordion playing (e.g. body gesture, leg movement, etc).
Choosing a piano accordion only gives you an imagined advantage up to 1/3 of all the skills needed for actually playing. It's proven by your own experience according to your post: you found playing some simple tunes with your right hand was easier but playing with both hands together was hard.
But actually piano background doesn't give you much when playing a piano accordion because the size, shape and mechanism of the piano keyboard are totally different from real piano keys, not to mention that the keyboard orientation is totally different from a piano.
Of course I am not saying piano skills are not useful at all, but they are only when you have a really professional piano background. For example if you have mastered all scales, arpeggios and chords on all 12 Major keys and 12 minor keys then your comprehensive knowledge of piano geography will help you a lot in the piano accordion playing.
Besides that, the real advantages when you choose to learn a new instrument are
1.Your knowledge of music theory.
2.Your passion for music and for the new instrument.
3.If you have a beautiful wife who is a professional musician.
Obviously you got all of them so the choice between accordion/bayan should be made from free will, not from whether you have a piano background.
And secondly, there is a very deep bayan culture in Russia. Bayan has an educational and esthetical state equal to violin and piano in Russia. Many people don't know that and think Russain bayan is just a normal instrument like CBA in Europe. But the educational resources and communities of bayan are far superior to piano accordion in Russia. Of course I am not a Russian so I can be wrong. Please tell me if I got a wrong picture. For me living in Russia is really a good reason to learn bayan.
I am not saying bayan is 100% better than piano accordion but it does have many advantages. You can google that or search in this forum.
And buttons are not so hard. I have some years' piano background but I chose bayan (C-system) right after I decided to play a bellow instrument. Only few days later I found that's a super right decision.
And about the free bass, I don't really think that one should learn standard bass BEFORE free bass. Again this should be a call by free will because they are totally different. Mastering the standard bass won't give you any advantage in learning free bass system, and vice versa. Actually having piano background will give you some advantages in learning free bass system because it's just like the piano keyboard, especially in Russian bayan (B-system) which lower notes are on your little finger side and higher notes are on the thumb side.
And again Russain bayan (and its education) is strongly connected to free bass system so having a bayan with free bass system is always a better choice. At least you'll have a converter switch which can produce cool sound when pressing it.