feat: add chat cost analytics backend (#23036)

Add cost tracking for LLM chat interactions with microdollar precision.

## Changes
- Add `chatcost` package for per-message cost calculation using
`shopspring/decimal` for intermediate arithmetic
- **Ceil rounding policy**: fractional micros round UP to next whole
micro (applied once after summing all components)
- Database migration: `total_cost_micros` BIGINT column with historical
backfill and `created_at` index
- API endpoints: per-user cost summary and admin rollup under
`/api/experimental/chats/cost/`
- SDK types: `ChatCostSummary`, `ChatCostModelBreakdown`,
`ChatCostUserRollup`
- Fix `modeloptionsgen` to handle `decimal.Decimal` as opaque numeric
type
- Update frontend pricing test fixtures for string decimal types

## Design decisions
- `NULL` = unpriced (no matching model config), `0` = free
- Reasoning tokens included in output tokens (no double-counting)
- Integer microdollars (BIGINT) for storage and API responses
- Price config uses `decimal.Decimal` for exact parsing; totals use
`int64`

Frontend: #23037

coderd/database/migrations/000435_add_cost_to_chat_messages.down.sql

@@ -0,0 +1,3 @@
+DROP INDEX IF EXISTS idx_chat_messages_created_at;
+
+ALTER TABLE chat_messages DROP COLUMN total_cost_micros;

coderd/database/migrations/000435_add_cost_to_chat_messages.up.sql

@@ -0,0 +1,68 @@
+ALTER TABLE chat_messages ADD COLUMN total_cost_micros BIGINT;
+
+WITH message_costs AS (
+    SELECT
+        msg.id,
+        ROUND(
+            COALESCE(msg.input_tokens, 0)::numeric * COALESCE(pricing.input_price, 0)
+            + COALESCE(msg.output_tokens, 0)::numeric * COALESCE(pricing.output_price, 0)
+            + COALESCE(msg.cache_read_tokens, 0)::numeric * COALESCE(pricing.cache_read_price, 0)
+            + COALESCE(msg.cache_creation_tokens, 0)::numeric * COALESCE(pricing.cache_write_price, 0)
+        )::bigint AS total_cost_micros
+    FROM
+        chat_messages AS msg
+    JOIN
+        chat_model_configs AS cfg
+    ON
+        cfg.id = msg.model_config_id
+    CROSS JOIN LATERAL (
+        SELECT
+            COALESCE(
+                (cfg.options -> 'cost' ->> 'input_price_per_million_tokens')::numeric,
+                (cfg.options ->> 'input_price_per_million_tokens')::numeric
+            ) AS input_price,
+            COALESCE(
+                (cfg.options -> 'cost' ->> 'output_price_per_million_tokens')::numeric,
+                (cfg.options ->> 'output_price_per_million_tokens')::numeric
+            ) AS output_price,
+            COALESCE(
+                (cfg.options -> 'cost' ->> 'cache_read_price_per_million_tokens')::numeric,
+                (cfg.options ->> 'cache_read_price_per_million_tokens')::numeric
+            ) AS cache_read_price,
+            COALESCE(
+                (cfg.options -> 'cost' ->> 'cache_write_price_per_million_tokens')::numeric,
+                (cfg.options ->> 'cache_write_price_per_million_tokens')::numeric
+            ) AS cache_write_price
+    ) AS pricing
+    WHERE
+        msg.total_cost_micros IS NULL
+        AND (
+            msg.input_tokens IS NOT NULL
+            OR msg.output_tokens IS NOT NULL
+            OR msg.reasoning_tokens IS NOT NULL
+            OR msg.cache_creation_tokens IS NOT NULL
+            OR msg.cache_read_tokens IS NOT NULL
+        )
+        AND (
+            pricing.input_price IS NOT NULL
+            OR pricing.output_price IS NOT NULL
+            OR pricing.cache_read_price IS NOT NULL
+            OR pricing.cache_write_price IS NOT NULL
+        )
+        AND (
+            (msg.input_tokens IS NOT NULL AND pricing.input_price IS NOT NULL)
+            OR (msg.output_tokens IS NOT NULL AND pricing.output_price IS NOT NULL)
+            OR (msg.cache_read_tokens IS NOT NULL AND pricing.cache_read_price IS NOT NULL)
+            OR (msg.cache_creation_tokens IS NOT NULL AND pricing.cache_write_price IS NOT NULL)
+        )
+)
+UPDATE
+    chat_messages AS msg
+SET
+    total_cost_micros = message_costs.total_cost_micros
+FROM
+    message_costs
+WHERE
+    msg.id = message_costs.id;
+
+CREATE INDEX idx_chat_messages_created_at ON chat_messages (created_at);