Fix Anthropic usage double-counting cache in input - #617
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Problem
Anthropic's message_start/message_delta stored input_tokens verbatim, but Anthropic's input_tokens already includes cache reads+writes. total_tokens was then recomputed as input+output+cache_read+cache_write, double-counting cache (e.g. input=100, cache_read=40, cache_write=25 → total=172). Every OpenAI-family path (openai_compatible, openai_codex) instead stores fresh input = max(0, input - cache_read - cache_write). Downstream consumers (session_stats.py:83, session_usage.py, context_window.py:183, _response_cost) all assume the fresh convention, so Anthropic silently over-reported stats and overcharged cost.
Fix
store fresh input in both _usage_from_message_start and _apply_message_delta_usage, matching the OpenAI convention; total_tokens computed from fresh input.
Tests
test_tau_ai.py updated to the corrected numbers (input 100→35, total 172→107); test_session_stats.py already encodes the correct convention, unchanged.
Validation
uv run pytest tests/test_tau_ai.py tests/test_session_stats.py (89 passed).