The background is perfect! What do you mean less busy? You’ve made an excellent photo of one of these funny fuzzballs.
Don’t get me wrong, I’m very fond of this picture (I wouldn’t have posted it otherwise), but the couple of thin branches directly behind the bird break its silouhette a bit. The rest is 100% to my liking.
That’s just nature. You can’t force that birb to sit higher on the branche. So I wouldn’t worry about it,