When extended thinking is enabled, the websearch interception agentic loop
builds a follow-up assistant message with only tool_use blocks. Anthropic's
API requires assistant messages to start with thinking/redacted_thinking
blocks when thinking is enabled, causing a 400 Bad Request.
Extract thinking blocks from the model's initial response, thread them
through the agentic loop, and prepend them to the follow-up assistant
message — matching the pattern used by anthropic_messages_pt in factory.py.
Fixes the error: "Expected 'thinking' or 'redacted_thinking', but found
'tool_use'"
The websearch interception handler was passing internal flags like
`_websearch_interception_converted_stream` to the follow-up LLM request.
This caused "Extra inputs are not permitted" errors from providers like
Bedrock that use strict Pydantic validation.
Fix: Filter out all kwargs starting with `_websearch_interception` prefix
before making the follow-up anthropic_messages.acreate() call.
giulio-leone