WebFetch/WebSearch fail with "400 adaptive thinking is not supported on this model" under Sonnet medium

Description

WebFetch and WebSearch consistently fail with the same API error, reproducible across multiple attempts and different URLs/queries:

API Error: 400 adaptive thinking is not supported on this model

Environment

• Model: Sonnet, "medium" reasoning effort
• Reproduced 5+ times across WebFetch and WebSearch, different URLs and queries, same error every time

What I ruled out

• Not a network/connectivity issue — curl to the same URLs succeeds (200 OK) from the same machine/session
• Not a specific-URL issue — reproduces across different domains and with plain search queries

Suspected cause

WebFetch's own tool description states it "processes fetched content using a small, fast model" — a separate internal API call for summarization. The error strongly suggests that internal call is passing an "adaptive thinking" parameter the underlying model/tier doesn't support, specific to the Sonnet-medium configuration.

Expected behavior

WebFetch/WebSearch should work normally under Sonnet medium, or fail with a clearer error if this reasoning-effort tier genuinely isn't supported for these tools.