fix: remove erroneous dollar-sign from BrightDataSearchTool search URLs and expose results_count in schema

[octo-patch]

Fixes #5269

Problem

BrightDataSearchTool.get_search_url used JavaScript template-literal syntax inside Python f-strings. Python treats $ as a literal character, so every constructed URL contained a stray dollar sign:

• Google: https://www.google.com/search?q=$hello%20world
• Bing: https://www.bing.com/search?q=$some+query
• Yandex: https://yandex.com/search/?text=$query

This caused all SERP searches to fail because the search engine received $<query> instead of the actual query string.

Additionally, results_count was read from **kwargs with a hard-coded default of "10", making it completely invisible to the Pydantic schema. Agents had no way to control the number of results returned.

Solution

1. Removed the $ prefix from all three f-string URL templates in get_search_url.
2. Added results_count to BrightDataSearchToolSchema as a typed int | None field with default=10, so agents can explicitly pass the desired number of results.
3. Added results_count as an explicit parameter to _run, replacing the hidden kwargs.get("results_count", "10") pattern.
4. Added tests verifying correct URL construction and results_count handling.

Testing

New unit tests added to brightdata_serp_tool_test.py:

• test_get_search_url_google — verifies no $ in Google URL
• test_get_search_url_bing — verifies no $ in Bing URL
• test_get_search_url_yandex — verifies no $ in Yandex URL
• test_run_default_results_count_is_10 — verifies default num=10
• test_run_with_custom_results_count — verifies custom count is forwarded

Note: This PR was created with AI assistance. Per the CONTRIBUTING.md guidelines, the llm-generated label should be applied (label does not yet exist in the repo).