**Describe the bug**

Routing Claude Code through LiteLLM to AWS Bedrock via `ANTHROPIC_BASE_URL` with `websearch_interception` configured, the interception short-circuit never fires. The `web_search_20250305` tool is forwarded to Bedrock, which rejects it because Bedrock does not support that tool on any API path.

There are two related problems here, which I want to separate clearly:

**Problem 1 (current, v1.83.7-stable):** On main today, interception does not fire for Claude Code's `web_search_20250305` request shape when routed through the Bedrock pass-through. This appears to be a tool-name / request-format compatibility gap — Claude Code sends the tool as `{"type": "web_search_20250305", "name": "web_search"}`, but the interception detection logic in current main doesn't recognize this as a search-only request that should be short-circuited. Related context in #21733 (adapter path) and #20179 (tool name detection on v1.81.3).

**Problem 2 (pending, PR #25242):** PR #25242 is attempting to fix the Claude Code compatibility gap — renaming the injected tool name to `WebSearch`, returning native Anthropic format (`server_tool_use` + `web_search_tool_result`), and adding streamin…