I can play violin by ear, meaning that if someone plays me a melody I can generally play it back note-for-note fairly quickly. I also can hear most common chord

I can play violin by ear, meaning that if someone plays me a melody I can generally play it back note-for-note fairly quickly. I also can hear most common chord progressions. I do not have perfect pitch, so I struggle with series of random notes and note clusters. What does it feel like? It feels the same as how you can just sing happy birthday without having to do any calculation about what note or lyric comes next. You can hear the song in your head and sing it. I also feel that the notes map into a grid and I will have songs mapped out by intervals. If you want to become better at playing by ear, you can improve rapidly with rigorous training. This is how I like to learn. I think it's much faster than just plunking around with your instrument and rediscovering everything for yourself, but may be less fun for you. Ultimately, you should do what you enjoy and avoid burning yourself out. I spend about 30% of my time on technical mastery of my instrument. Right and left hand technique, scales, arpeggios, chords, speed. Another 30% is spent working on repertoire. These are songs where I already have all the notes worked out or written down. This is where you learn to polish your work to the point where it can be performed. The remaining 40% is consists mostly of transcription and improvisation. I do some ear training as well. Transcription is very painful for most beginners, but you quickly improve at it. I cannot stress how invaluable transcription is for improving your ear. You say you "slowly work things out by trial and error". This will pay HUGE dividends if you keep it up! For improvisation, I suggest recording a backing track playing simple chords very slowly and attempting to improvise. I try to have some guiding idea, like trying to arpeggiate over all the chords, or only move in half or whole steps but always land on a chord tone, or always land on the third of the chord. As you get better, you can speed up your backing tracks and work on more complex chord progressions. Knowing your scales and arpeggios will really help here. The more comfortable you are with the layout of your instrument, the easier improvising will be. I'll stop with this piece of advice -- plan your practice sessions! It doesn't matter how you break them up, as long as you are consciously working on something specific. Staying organized and having a plan will ensure that you continue to improve and help combat the plateau that many amateur musicians encounter.