OK, at home, had a quick play. Nothing drastic - just selected the background in LRC using masks and darkened it a tiny bit and added some warmth. Did 2 linear gradient masks at the top to darken them a bit more since they are much brighter than the L/R sides of the background around the bird.
In Photoshop, I just cropped (unrestrained) to remove the clutter at the bottom RH corner. I extended the canvas and used both content aware fill and generative fill (the former for the top section and the Left hand side extension using generative).
It's not 3:2 original. I did play with that, but couldn't get it to work and cut out that messy bit at the bottom RH corner. Going too tight means no breathing space in front of the bird and then the composition looks awkward. Fixing that means cutting its back off, which isn't pleasing either imho.
I'm not happy with omitting the branch that it was perched on either.
Ideally, cloning out the messy sections at the bottom RH would have been the best option, but my cloning skills aren't l33t enough for that at this point of time in my editing experience LOL.
I didn't touch the colours of the bird or make any changes to the bird. It is identical to the bird in your original shot in terms of exposure and colour temperature/hue/saturation, etc. I feel that the colours of the bird as per the original are very accurate. They may appear boring and bland and lack "vibrancy" but the colours are indeed accurate, at least to what my eyes tell me.
A slightly looser shot would have helped I think, but hindsight is wonderful isn't it LOL!
Cheers,
Dave
edit: I know your name from somewhere but I can't for the life of me remember where. Do you post on the Brisbane Birds Facebook page perhaps?