test: enable mypy checks for fetcher tests

[samrusani]

Related Issues

• Part of Run typing checks on our test files #10396

Proposed Changes:

• add the focused LinkContentFetcher test module to the mypy target
• give the lifecycle tests explicit sync and async client mocks so mypy can verify their close assertions without ignores or casts

How did you test it?

• hatch run test:types test/components/fetchers/test_link_content_fetcher.py — passed, no issues in 1 source file
• hatch run test:unit test/components/fetchers/test_link_content_fetcher.py -m "not integration" — 26 passed, 7 deselected
• hatch run fmt-check test/components/fetchers/test_link_content_fetcher.py — passed
• git diff --check — passed

Notes for the reviewer

• This is a test-only increment of the typing umbrella issue, so it intentionally does not close Run typing checks on our test files #10396.
• No release note is included because the change is limited to tests and type-check configuration; a maintainer can apply ignore-for-release-notes if needed.
• AI assistance disclosure: this PR was fully generated with AI assistants. A separate assistant independently reviewed the exact commit, and the focused checks above were run on that commit before publication.

Checklist

• I have read the contributors guidelines and the code of conduct.
• I have updated the related issue with the scoped increment.
• I have added unit tests and updated the docstrings. (No behavior changed; this increment type-checks existing tests.)
• I've used a conventional commit type for the PR title.
• I have documented my code. (Not applicable to this test-only typing change.)
• I have added a release note file. (Test-only change; see reviewer note.)
• I have run all pre-commit hooks. (Focused mypy, unit, formatting, and diff checks are listed above.)

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