Alex,
I would consider casting your net wider than just Canon - you should be able to get the Apps you like for your Smartphone and iPad for most modern camera systems.
I agree with others that once you start photographing birds, it's a slippery slope, and those little geewhizzits will get you in - to the point where you will easily seriously consider all manner of better, more expensive and heavier gear! :eek!: :king: :cat:
I think it may be difficult to get a great performing system at your budget, I would suggest trying to up it a little more .... some of the less capable entry level gear can be an exercise in frustration for anything that doesn't sit cooperatively still in idealized bright light .....
One thing I will mention is that is that you will often want a longer lens than the one you have, and 600-1200mm is not out of the question! :cat:
The other thing, is that although photographic perfection can take a seeming lifetime to, well ..... 'perfect' --- that you can be up and running and taking good images quite easily - largely automated ....
As a minimum, I would suggest the 20MP Sony RX10 III bridge camera for a little more than your stated budget. Excellent quality, with a superb Zeiss lens which zooms from 24-600mm, and can even be cropped in-camera (or digitally zoomed) to 900mm and 1200mm without loss of image quality at reduced file sizes of 10MP and 5MP respectively - basically you just throwaway the background to be left with the subject bird. Great review well worth reading here:
http://www.kenrockwell.com/sony/rx10-iii.htm
The only other better set up I would recommend is as has been already roughly mentioned - the 24MP Nikon D7200 + Sigma 150-600mm f6.3 Contemporary. This camera body is recently superceded so you should be able to pick a pretty good deal new. It offers superb performance and probably the best photography bang for the buck on the market. Being an APS-C sized sensor it turns the 150-600 into a 225-900mm lens. Also there is a 1.3x crop mode in-camera which means your lens becomes 300-1200 ! Very nice indeed!!
https://m.dpreview.com/reviews/nikon-d7200
Many Canon shooters envy the Nikons better sensor performance, and the Nikons at this level and above have some of the best 3D AF tracking in the business. This setup will be nearly double your budget, but we'll worth it - it will serve you well for many many years.
I shoot a similar rig (check my gallery to see what you could expect), and easily carry it around all day on a Black Rapid sling, and nearly always shoot handheld.
You might get an even better lens for slightly more, and a bit more weight, but faster aperture, in the Nikon 200-500 f5.6. If you wanted true Pro level performance, for double the D7200's price the new Nikon D500 is unbeatable - you get a higher frame rate, and state of the art AF, but no better IQ in practice.
Good luck!
Chosun :gh: