### What happened?

When websearch interception runs on the `/v1/messages` path, the search results never reach a streaming client.

Interception forces `stream=True` → `stream=False` so the agentic loop can inspect the response. After the loop, `_inject_native_blocks` prepends `web_search_tool_result` blocks to the response (added so Anthropic-native clients can render citations), and the response is re-wrapped for the caller by `FakeAnthropicMessagesStreamIterator`.

That iterator only knows four content block types:

```python # litellm/llms/anthropic/experimental_pass_through/messages/fake_stream_iterator.py if block_type == "text": ... elif block_type == "thinking": ... elif block_type == "redacted_thinking": ... elif block_type == "tool_use": ... content_block_stop = {"type": "content_block_stop", "index": index} ```

There is no `else` branch. For a `web_search_tool_result` or `server_tool_use` block it emits **only** `content_block_stop` — no `content_block_start`, no delta, no payload. The blocks are silently dropped.

So the two features work against each other: interception is the only thing that sets the converted-stream flag, and it is also the only thing that produces…