You played this well and show fluency with your notes, so how to improve it? At the moment your left hand is competing with your right hand to be heard. So although you might find it difficult to tone down your left hand at first, if you keep thinking about it while you are playing, it will eventually begin to happen.
Something else I would suggest is to consider triple time. In three time, the first note is the strongest while the second and third beats are lighter. I don't know if you have ever danced the waltz, but if you watch a dancer, they sink into the first beat and then go up on the toes for the second and third beats. You could perhaps think of bouncing a ball. The first bounce as it hits the ground is the strongest and the next two bounces become progressively weaker. So I would suggest sinking/leaning into the first beat and then loosening and slightly raising your left wrist (like the drop/slur) technique) for the second and third beats. This would also apply to the right hand where you have repeated notes, as in the first bar.
Something else you might like to try is phrasing the melody into two bars instead of seeing each bar as a individual box. For instance, for the first four bars you could say/sing "I like to play this piece, I like to play this piece." If you think about how you would say this, taking note of the flow of each phrase, it will help your right hand to sound more fluent. You would naturally put slightly more emphasis on the word 'I' and slightly less emphasis on the words 'like to'. In the same way, the whole phrase is moving towards the word 'play'. I like to PLAY this piece. You would naturally lean towards the word 'play' so your hand would be trying to imitate the sound of your voice, moving towards the note representing 'play'.
So if your left hand stops competing with your right hand, and you think of the natural movement of strong/weak/weak in your left hand, and move towards the most important notes (thinking of sentences) this piece will improve immediately.
I hope this helps.