The struct field alone never reached the wire: the raw passthrough
pipeline is covered by enableMixedGeminiToolInvocations (#5711), but
TransformClaudeToGeminiWithOptions builds GeminiToolConfig from scratch
and never set the flag, so gemini-* models entering through the Claude
format gateway could still hit the upstream 400 from issue #5709.
- Set IncludeServerSideToolInvocations=true when the built tool
declarations mix functionDeclarations with googleSearch, matching the
raw-path injection semantics.
- Replace the marshal-roundtrip-only test with behavior tests that
drive TransformClaudeToGeminiWithOptions: mixed tools set the flag,
function-only and web-search-only requests leave it unset.