[BUG设计工程师 (hackermengzhi)]

Why are these changes needed?

Opening a new path leaves FileSurfer's previous search active. After searching file A, opening file B and searching for the same term can skip file B's first viewport; find_next() also reuses a query that was never started on file B.

set_path() assigns two unused public attributes instead of clearing the private search fields read by find_on_page() and find_next(). Reset those fields on navigation. Add public-behavior regressions for clearing an old query and searching the first viewport of a new file, plus a control for cycling matches within one file.

Validation on Python 3.12.13:

• New regressions before fix: 2 failed, 1 passed.
• After fix: 5 passed across the new browser tests and existing FileSurfer agent tests, using the repository's locked OpenAI version (1.93.0).
• Ruff 0.4.8 lint and formatting checks passed for the changed Python files.

Related issue number

No existing issue found for search-state reset on navigation.

Checks

• I've included any doc changes needed for https://microsoft.github.io/autogen/. Existing navigation behavior is restored; no API change.
• I've added tests (if relevant) corresponding to the changes introduced in this PR.
• I've made sure all auto checks have passed.

[BUG设计工程师 (hackermengzhi)]

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