fix: token accounting (cachedWriteTokens & cacheWriteInputTokens)

[joshlarsen]

Summary

Fix cache-write token accounting by separating cache writes from ordinary input and exposing them through ACP's cachedWriteTokens field.

Fixes #509. The cachedWriteTokens omission is also mentioned in #447.

The change also:

• includes cacheWriteInputTokens in quota metadata;
• displays cache reads and writes separately in /status;
• treats a missing cache-write value as zero for older binaries supplied through CODEX_PATH;
• leaves total, output, and reasoning counts unchanged.

Token calculation

Codex reports inputTokens inclusive of cache reads and writes. The normalized categories are therefore:

ordinary input = inputTokens - cachedInputTokens - cacheWriteInputTokens
cache read     = cachedInputTokens
cache write    = cacheWriteInputTokens
output         = outputTokens
total          = ordinary input + cache read + cache write + output

Reasoning tokens are already included in outputTokens, so reasoningOutputTokens is exposed as ACP thoughtTokens but is not added again.

For example:

Codex: input=100, cache-read=40, cache-write=30, output=10, reasoning=5, total=110
ACP:   input=30,  cache-read=40, cache-write=30, output=10, reasoning=5, total=110

The mapping is:

Codex	ACP
inputTokens - cachedInputTokens - cacheWriteInputTokens	inputTokens
cachedInputTokens	cachedReadTokens
cacheWriteInputTokens	cachedWriteTokens
outputTokens	outputTokens
reasoningOutputTokens	thoughtTokens
totalTokens	totalTokens

Compatibility

cacheWriteInputTokens is required by the current generated app-server type. At runtime, a missing value from an older CODEX_PATH binary is normalized to zero. Invalid negative partitions are not clamped, so inconsistent upstream counters remain observable.

Validation

• npm run typecheck
• npm test — 609 tests passed
• npm run build
• Live Codex smoke test confirmed 3 ordinary input + 11,099 cache-write + 5 output = 11,107 total.

OpenAI references

• Prompt caching guide: monitor cache performance documents cached_tokens, cache_write_tokens, and the ordinary-input subtraction formula.
• Responses API reference defines response usage fields, including input-token details.