Fix private registry authentication for aiodocker image pulls (#6355)

* Fix private registry authentication for aiodocker image pulls

After PR #6252 migrated image pulling from dockerpy to aiodocker,
private registry authentication stopped working. The old _docker_login()
method stored credentials in ~/.docker/config.json via dockerpy, but
aiodocker doesn't read that file - it requires credentials passed
explicitly via the auth parameter.

Changes:
- Remove unused _docker_login() method (dockerpy login was ineffective)
- Pass credentials directly to pull_image() via new auth parameter
- Add auth parameter to DockerAPI.pull_image() method
- Add unit tests for Docker Hub and custom registry authentication

Fixes #6345

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <noreply@anthropic.com>

* Ignore protected access in test

* Fix plug-in pull test

* Fix HA core tests

---------

Co-authored-by: Claude <noreply@anthropic.com>

tests/plugins/test_plugin_base.py

@@ -369,7 +369,7 @@ async def test_load_with_incorrect_image(
     with patch.object(DockerAPI, "pull_image", return_value=img_data) as pull_image:
         await plugin.load()
         pull_image.assert_called_once_with(
-            ANY, correct_image, "2024.4.0", platform="linux/amd64"
+            ANY, correct_image, "2024.4.0", platform="linux/amd64", auth=None
         )
 
     container.remove.assert_called_once_with(force=True, v=True)