I had the same setup as @Connor Cochrane and @Aaron, Canon 7Dii with the 100-400ii and extender and if I was shopping for a good setup, that's exactly what I would buy again. I had over extended my spending at the time and had to let my good gear go for a while. I thought it was a great setup for birding and wildlife photography in general. One advantage the 100-400ii has over the 400mm F/5.6 prime lens that I used to have is the closer minimum focus distance. You can zoom to 400mm and focus from approximately 3 feet away, which is great for shooting insects and any birds that might land closer than 12 feet away, which is the 400mm prime lens's minimum focus distance.
When I started looking for a replacement camera a year or so later, I came across a used full frame Canon 5Diii with a 24-105 F/4 L lens, flashes and other accessories that I was going to pair with another 100-400ii when funds allowed. Well, I came across what I considered to be a deal on a 300mm F/2.8 lens and put a 1.4iii extender on it to give me 420mm of reach at f/4. I'm quite happy with my current setup but I honestly think I'd trade it for my old setup, mostly for the extra reach of the longer lens and crop factor. The 100-400mm and 1.4 extender is 560mm with a 1.6 crop factor giving a focal length of 896mm in 35mm equivalent for my old setup compared to my current setup's 420mm focal length.
Canon 5D Mark iii with 300mm f/2.8 L prime lens and 1.4x Mark iii extender is my current setup.
Canon 7Dii with 100-400mm Mark ii, with or without the 1.4x Mark iii extender, would be my recommended setup.