Camera recommendations for the avid birder

Ive had my Canon Powershot SX720 HS for about two years now. I originally bought this camera for its portable and lightweight features. There were some downsides though.
1: It did not/ does not come with zoom lenses. For a birder this can be tricky, especially when trying to take far away shots.
2: It does not have clear focus.

I would like my next choice to be lightweight, portable, have clear focus, to come with zoom lenses, and overall be in a price range of about $300- $500.
If you have any recommendations, please post a comment below.