fix: remove $ prefix from f-strings in BrightDataSearchTool.get_search_url

[devin-ai-integration]

Summary

Fixes #5269

The get_search_url method in BrightDataSearchTool used JavaScript template literal syntax (${query}) instead of Python f-string syntax ({query}) when building search URLs. This caused every search query to be prepended with a literal $ character (e.g. ?q=$AI%20news instead of ?q=AI%20news). All three search engines (Google, Bing, Yandex) were affected.

The fix removes the erroneous $ from all three f-strings.

Added 4 tests to cover the fix:

• Unit tests for get_search_url on each engine verifying correct URL format
• Integration test through _run verifying the URL sent to the API has no $ prefix

Review & Testing Checklist for Human

• Verify the three f-string changes in brightdata_serp.py lines 133-137 look correct (removed $ only, nothing else changed)
• Optionally run BrightDataSearchTool with a real API key to confirm queries work end-to-end without the $ prefix

Link to Devin session: https://app.devin.ai/sessions/0f820d69f9f74596a25ecab76c3fed67

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Note

Low Risk
Low risk: fixes a small URL formatting bug and adds focused tests; behavioral change is limited to removing an unintended $ character in outgoing search queries.

Overview
Fixes BrightDataSearchTool.get_search_url to use proper Python f-string interpolation ({query}) for Google/Bing/Yandex, removing the accidental literal $ prefix that was being sent in search queries.

Adds unit tests for each engine’s URL formatting and an _run flow test to assert the request payload URL is encoded correctly and contains no $ in the query.

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[devin-ai-integration]

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