Cache-read tokens are priced at the full input rate — overstates cost ~10x on the cached path #268

The bug

lib/ai-pricing.ts says it outright:

// Cache reads bill at the input rate here (we already fold cache_read/creation
// into `input` in user-ai.ts), which slightly over-estimates cached calls

"Slightly" is doing a lot of work. Anthropic bills cache reads at ~10% of the input rate and cache writes at 1.25×. Folding both into input at the full $3/M is a 10× overcharge on the read path.

Live 30d ledger, chat kind: input=4,796,074, of which cache_read=993,574. Those tokens are charged ~$2.98 and really cost ~$0.30 — about $2.68 overstated on one kind alone, ~7% of the reported total. The ratio gets worse as prompt caching does its job, so the error grows precisely as the platform gets more efficient.

Fix

1. Stop folding cache_read_input_tokens / cache_creation_input_tokens into input in user-ai.ts — carry them as their own fields.
2. Add cacheReadPerM / cacheWritePerM to the PRICES table (Anthropic: 0.1× and 1.25× of input).
3. Price the three components separately.
4. Storage: ai_usage has input_tokens/output_tokens only. Add nullable cache_read_tokens/cache_write_tokens columns in a migration; existing rows stay NULL and keep their historical (over-stated) cost rather than being retro-corrected.

Acceptance

• Cache reads priced at the cache rate, not the input rate; unit test with a known Anthropic usage block.
• Historical rows unchanged — no retroactive rewrite of a ledger.
• Usage page can show the cached share, since it is now the interesting number (it is the saving).

Note the sign: this makes reported cost go down. It does not offset #267, which makes it go up by more.