fix: sync Claude Desktop profile during proxy takeover (#3157)

* fix: sync Claude Desktop profile during proxy takeover

* fix(provider): skip Claude Desktop backup refresh during takeover

- Route Claude Desktop takeover updates directly through the 3P profile writer.
- Keep takeover startup backup state unchanged when provider metadata changes.
- Narrow platform-specific test helpers and environment setup with cfg gates.

* fix(provider): restore PathBuf import for CI tests

- Restore an unconditional PathBuf import for provider tests.

- Keep Linux cargo test builds compiling while preserving Claude Desktop cfg-gated helpers.

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Co-authored-by: Jason <farion1231@gmail.com>