What kind of zoom lense for bird photography?

Ok so i am pretty new to photography but i am getting better. I am mostly interested in bird photography. I have taken many pictures of birds in my backyard from hummingbirds to pileated woodpeckers. The crows are too scared lol
So i am looking for a lense with good zoom, at least 400mm. My current zoom lense is 55-200mm.

So my camera is a nikon d3300. I need a lense with at least 400mm zoom for photographing wild birds. I would like to photograph other animals too but i currently dont have the opportunity to. The lense cant be very expensive because i am a teenager and unless it is under $100 (ebay?) my parents will choose whether they want to pay it or not.

I put a picture i took of a hummingbird. The picture is compressed so it is blurry when you zoom into it. But the actual picture is very good.

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Does the Nikon 105mm Macro lens work also as a zoom lens in a Dslr camera?

Does the Nikon 105mm Macro lens work also as a zoom lens in a Dslr camera?
Added (1). I like taking macro pictures, and have a 40mm macro lens. The only thing I miss in the 40mm lens I have, is the lack of VR.
I use this lens as a prime all occasions lens.
I do a lot of macro shootings, but I also like a lens that is versatile.
I was thinking also about the 18-300mm lens, which is quite compact… But I dont know how if I can take good macro with this.
Big doubt… Lol

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Which is fast at focusing nikon or canon?

"For beginner dslr's"

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Should I invest in a better camera body or lense?

I have a ~$2000 budget for camera gear and my shots will mostly be for a local newsletter. I want the ability to shoot all kinds of shots from sports (which may need telephoto) to portraits (which would benefit from high aperture lenses).

Assuming I wanted to go Canon, i'm thinking of investing in a mid-range DSLR camera body (like a 70D) and maybe a cheap telephoto lense to go along with the kit lense. Or I could buy a lower-tier body (like a T5i) and go with a better walkaround lense instead, or maybe even a ~50mm prime and a better telephoto.

What are your thoughts?

Read more: Should I invest in a better camera body or lense?