Advice wanted for camera upgrade.
I have a Canon Eos550D that I've used since buying it in 2011 or so. I have 3 lenses, of which i mostly use 2: Canon zoom lens EF 75-300mm 1:4-5.6 IS and EFS 18-135mm with image stabilizer nano usm. The third is a macro lens (10-18mm). Recently, I've been considering getting either a new camera, new lenses, or both. This is due to picking up more bird photography and volunteering taking pictures of dogs for a local shelter and not being satisfied with my camera's capabilities. often the images are quite grainy/pixelated.
For the bird side I'm looking at getting a bigger lens and have seen recommendations for that to be a 600mm lens or so. But for the dog photography side, i need something that takes good portraits with nicely blurred backgrounds and also can handle some action shots of them running at/past me.
The debate for me is if i get a new body, most that i saw were all RF, so then i would have to get multiple new lenses as well. Is there a mid-range body that's EF that's a good upgrade in quality from what i have? or is it worth it to get a new body with a portrait and a distance lens? If i get a higher mm lens for birding, which kind of lens would be best and would it make sense to have the range of 18-135, 75-300 and one around 600mm or skip the middle one?
in terms of budget, i don't want to spend more than a 3 or 4k euros total.
Thanks