feat(cost): itemize reasoning cost per span and by model

[JoniMartin27]

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What

Lookspan already bills reasoning tokens at their own rate, but the cost was blended into the per-span total. This makes the reasoning cost a first-class, queryable figure — per span and per model.

• computeCostBreakdownUsd(model, usage) returns { total, reasoning }. computeCostUsd is now a thin wrapper, so existing behavior/signature is unchanged.
• enrichSpanCost stores a per-span reasoning_cost_usd at ingest (additive migration v7; SQLite + Postgres parity verified in-process via pg-mem).
• CostsRepository.summary adds reasoning (total) and reasoningByModel (the routing dimension). GET /api/costs/summary surfaces both.
• Dashboard Costs view shows reasoning as a share of total cost and charts Reasoning cost by model.

The reasoning figure is computed even when a model has no explicit reasoningPer1M — it is then the share of the output bill those tokens account for, which is the very signal that tells you whether a dedicated reasoning rate is worth setting. It is always a sub-component of total, never an extra charge.

Why

In reply to the reasoning-token billing post, @alphaxagent.bsky.social noted:

Separate reasoning token billing makes the "use a smarter model on harder requests" routing strategy much more legible — you can now see exactly what the reasoning premium costs per request type, not just in aggregate.

This delivers exactly that: the reasoning premium is now visible per request type (per model), not just in aggregate.

Tests

• computeCostBreakdownUsd: explicit reasoning rate, output-rate fallback (total unchanged), zero-reasoning, unknown model.
• enrichSpanCost: itemizes reasoningCostUsd on the span.
• CostsRepository.summary + Postgres parity: reasoning total and reasoningByModel round-trip and sum.
• API: /api/costs/summary exposes the new fields.

npm run ci green locally: typecheck, lint (biome), 237 tests, build.

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