Serialize managed agent PATH tests

[wpfleger96]

Summary

• Add a shared test-only managed-agent PATH mutex helper.
• Serialize the discovery cache-refresh test with the existing readiness tests that mutate PATH.
• Keep the final diff scoped to the managed-agent test race fix.

Validation

• cargo test --lib managed_agents x3: 692 passed, 0 failed each run.
• just desktop-tauri-clippy: passed.
• cargo fmt --manifest-path desktop/src-tauri/Cargo.toml --all -- --check: passed.
• git diff --check: passed.
• pnpm check:file-sizes from desktop/: passed.
• Pre-push hook: desktop-test, mobile-test, rust-tests, desktop-tauri-test all passed.

Quality gate

• Minimalism: 9/10. The shared helper is load-bearing because it avoids raising the file-size exception while centralizing the exact lock behavior.
• Elegance: 9/10. The call sites now state intent with lock_path_mutex() rather than repeating poisoned-lock handling.
• Correctness: 9/10. Both PATH-mutating readiness tests and the PATH/cache discovery test now share the same process-global lock.