test: Update responses tests based on vllm testing

[msager27]

What does this PR do?

Updates a few responses integration tests based on testing with vLLM. Some context:

I initially tested with vLLM + Qwen3.5 as part of #5216. That PR was more of a staging effort and will be mostly obsoleted by #5297 and get closed. However, there are a few changes from that PR that I've pulled into separate PRs:

1. This PR which makes one of the web search tests more flexible in its validation (plus a couple skips when provider is vllm)
2. fix: add test_id to normalize_tool_request() to avoid hash collision #5233

Test Plan

Rerun the responses web search tests and verify they work as expected