I was in a similar situation with my Canon 500D and tamron 70-300 lens (which broke after a ribbon cable inside of it disconnected). I used the 70-300 mainly for wildlife photography, but also for macro, landscapes, and other general photography.

For your purposes, the 70-300 could be sufficient, but I would not get this lens specifically for bird photography unless you are able to get really close to birds. For general photography, wildlife, and occasional bird or macro, I would say it's an excellent lens. With a Canon 500d (T1i) and old tamron 70-300, I was able to get some pretty good shots, but they required extremely close distances to the subject:

A sigma 150-600 would be a much better choice for bird photography, but it is a bit unwieldy to carry around for general photography unlike the 70-300. It also won't let you get too close to your subject since the minimum focus distance is 8.5ft. It should have better IQ than the canon 100-400, does not have the push-pull dust problem, and has a very good zoom range, image stabilization, and autofocus. I bought mine here (prices fluctuate between 900-1000) and it has worked very well for me. It also comes with a simga dock, which allows you to update autofocus firmware and calibrate the the autofocus. A used canon 100-400 could also work, but it's a pretty old lens at this point. A main advantage would be that it is lighter and has the canon brand, if those are important factors for you. But if weight is an important factor and you do not care about the Canon brand, a new sigma 100-400 like this would probably be a better choice.