chore(db): backfill historical ai_usage costs after pricing fix

Re-prices every existing ai_usage row using the correct $/1M token rates
per model family. CASE clauses ordered specific-first (flash-lite before
flash) to mirror the longest-prefix-match in priceFor(). Aliases
(gemini-*-latest) resolve to the 2.5 family, the only one in production
during the affected window.

The grounding-fee component ($35/1k above 1500/day free tier) is not
recomputed: historical traffic shows zero grounded calls in the window,
so the bumper would be 0. Down is a no-op (irreversible by design — the
original miscalculated values are not preserved).

backend/migrations/000031_backfill_ai_usage_costs.down.sql

@@ -0,0 +1,4 @@
+-- Irreversible: the original (incorrect) per-row costs were not preserved.
+-- Rolling back would require recomputing at flash-lite rates, which is exactly
+-- the bug we just fixed. No-op.
+SELECT 1;

backend/migrations/000031_backfill_ai_usage_costs.up.sql

@@ -0,0 +1,29 @@
+-- Re-price historical ai_usage rows. Until the model-aware estimateCost fix
+-- (migration 000030 era), every call was billed at hardcoded flash-lite rates
+-- regardless of the actual model. This restates estimated_cost_usd using the
+-- correct $/1M token rates per model family.
+--
+-- Aliases (gemini-*-latest) are assumed to resolve to the 2.5 family — the only
+-- one in production at the time. The grounding-fee component ($35/1k above the
+-- 1500/day free tier) is intentionally not recomputed: historical traffic
+-- shows zero grounded calls in the affected window, so the bumper would be 0.
+--
+-- More-specific WHEN clauses come first (e.g. flash-lite before flash) to
+-- mirror the longest-prefix-match semantics of priceFor() in Go.
+
+UPDATE ai_usage
+SET estimated_cost_usd = ROUND((
+  CASE
+    WHEN model LIKE 'gemini-3.1-pro%'         THEN input_tokens * 2.00  + output_tokens * 12.00
+    WHEN model LIKE 'gemini-3.1-flash-lite%'  THEN input_tokens * 0.25  + output_tokens *  1.50
+    WHEN model LIKE 'gemini-3-flash%'         THEN input_tokens * 0.50  + output_tokens *  3.00
+    WHEN model LIKE 'gemini-2.5-pro%'         THEN input_tokens * 1.25  + output_tokens * 10.00
+    WHEN model LIKE 'gemini-2.5-flash-lite%'  THEN input_tokens * 0.10  + output_tokens *  0.40
+    WHEN model LIKE 'gemini-2.5-flash%'       THEN input_tokens * 0.30  + output_tokens *  2.50
+    WHEN model = 'gemini-pro-latest'          THEN input_tokens * 1.25  + output_tokens * 10.00
+    WHEN model = 'gemini-flash-latest'        THEN input_tokens * 0.30  + output_tokens *  2.50
+    WHEN model = 'gemini-flash-lite-latest'   THEN input_tokens * 0.10  + output_tokens *  0.40
+    ELSE estimated_cost_usd * 1000000  -- preserve original (will divide back below)
+  END
+) / 1000000.0, 6)
+WHERE provider = 'gemini';