usage-extension: rethink input/cache columns across providers

[tmustier]

Problem

The /usage table currently shows:

• Tokens = input + output
• ↑In = input
• Cache = cacheRead + cacheWrite

This is mechanically correct, but the ↑In column is misleading across providers.

Why it looks wrong

For Anthropic, prompt caching is reported roughly as:

• input = small non-cached remainder
• cacheWrite = new prompt tokens entering cache
• cacheRead = prompt tokens served from cache

For OpenAI/Codex, input tends to contain much more of the fresh prompt tail, and cacheWrite is often 0 in practice.

That makes the current UI look like:

• Anthropic: tiny ↑In, huge ↓Out
• OpenAI: large ↑In, moderate ↓Out

Even when the underlying prompt behavior is more similar.

What to decide

We should decide what ↑In is supposed to mean:

1. raw uncached input only (input) — current behavior
2. fresh input sent this turn (input + cacheWrite)
3. total prompt seen by the model (input + cacheRead + cacheWrite)
4. split the concept into separate columns / labels

Constraints

• cacheRead should not be folded into Tokens, because that double-counts repeated cache hits over time.
• cacheWrite is new input and may belong in ↑In, depending on the intended semantics.
• Labels should make cross-provider comparisons intuitive.

Suggested next step

Review a few real session examples from Anthropic and OpenAI/Codex, then choose the least surprising display model and update column labels/tooltips/help text accordingly.