Anthropic: capture prompt cache diagnostics (cache_miss_reason, cache_missed_input_tokens) #861

anthropic 1.9.0 made cache diagnostics GA: a diagnostics= request parameter and Message.diagnostics.cache_miss_reason, a union of reason types (model, system, tools or messages changed; previous message not found; unavailable), each carrying cache_missed_input_tokens. Beta BetaMessage.diagnostics already existed in 1.8.0 and isn't captured either.

Proposal

In py/src/braintrust/integrations/anthropic/tracing.py:

• Add "diagnostics" to METADATA_PARAMS so the request option is logged.
• In _log_message_to_span / _message_output, log message.diagnostics.cache_miss_reason.type as metadata.
• Record cache_missed_input_tokens as a numeric metric (e.g. prompt_cache_missed_tokens).
• Read the fields with getattr so older SDK versions (0.48.0) need no gating. Streaming should get this from the message_start snapshot.

Tests

New cassette-backed test: two calls, the second passing diagnostics={"previous_message_id": ...}.

Parent: #858 (found while reviewing the 2026-10-05 weekly dependency update, #849).

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