Several possibilities:

1. In the examples shown, it could be a problem with the subject. The center of the picture is a rather fuzzy plumage for the dove and sharp lines for the white-eye.
2. Your 55-250mm is not so sharp at the long end. Decent lens, but not built/checked to stringent specs like a L series. Only way to tell is to try another lens.
3. Your camera's AF is struggling. The AF works better when the lens has a wide max aperture. At the long end your lens max aperture is f/5.6, pretty close to the AF working limit (officially f/5.6, in practice f/6.3 with good light). Your 9-point AF is a fairly old tech, I had the same in a 450D (ten years ago). I improved all my lenses by moving to a more recent body with a much better AF.
4. The lens IS isn't doing miracles. At the long end very small residual moves can induce some blur.

To remove as many variables as possible from the equation, you can do a rough test of your gear:

• Tape a newspaper on a wall, under good lighting
• Put your camera+lens on a tripod if you have one, or on a table, sufficiently far from the wall (at bird shooting distance...) and aim the camera at the newspaper
• Use a remote trigger or use the 2-seconds timer on the shutter, so that you aren't touching the camera when it takes the picture.

If the image is sharp then your lens and AF are OK. Otherwise by giving some forward slant to the newspaper you can evaluate the amount of front-focus/back-focus (see which part of the page is really in focus) and take this in account when shooting the birds (pre-focus on some foliage before/beyond the bird).

Several possibilities:

1. In the examples shown, it could be a problem with the subject. The center of the picture is a rather fuzzy plumage for the dove and sharp lines for the white-eye.
2. Your 55-250mm is not so sharp at the long end. Decent lens, but not built/checked to stringent specs like a L series. Only way to tell is to try another lens.
3. Your camera's AF is struggling. The AF works better when the lens has a wide max aperture. At the long end your lens max aperture is f/5.6, pretty close to the AF working limit (officially f/5.6, in practice f/6.3 with good light). Your 9-point AF is a fairly old tech, I had the same in a 450D (ten years ago). I improved all my lenses by moving to a more recent body with a much better AF.
4. The lens IS isn't doing miracles. At the long end very small residual moves can induce some blur.

To remove as many variables as possible from the equation, you can do a rough test of your gear:

• Tape a newspaper on a wall, under good lighting
• Put your camera+lens on a tripod if you have one, or on a table, sufficiently far from the wall (at bird shooting distance...) and aim the camera at the newspaper
• Use a remote trigger or use the 2-seconds timer on the shutter, so that you aren't touching the camera when it takes the picture.
• Do one image (or a series of shots) with AF.
• In the same test conditions do another image using manual AF. For this use LiveView and zoom in. This can be a bit fiddly because the focus ring on the 55-250 is a bit coarse.

If the image with manual focus is sharp, your lens is OK

If the above and your AF image is also sharp then your AF is OK. Otherwise by giving some forward slant to the newspaper you can evaluate the amount of front-focus/back-focus (see which part of the page is really in focus) and take this in account when shooting the birds (pre-focus on some foliage before/beyond the bird).