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/dbmock/dbmock.go

@@ -1778,6 +1778,66 @@ func (mr *MockStoreMockRecorder) GetChatByIDForUpdate(ctx, id any) *gomock.Call
 	return mr.mock.ctrl.RecordCallWithMethodType(mr.mock, "GetChatByIDForUpdate", reflect.TypeOf((*MockStore)(nil).GetChatByIDForUpdate), ctx, id)
 }
 
+// GetChatCostPerChat mocks base method.
+func (m *MockStore) GetChatCostPerChat(ctx context.Context, arg database.GetChatCostPerChatParams) ([]database.GetChatCostPerChatRow, error) {
+	m.ctrl.T.Helper()
+	ret := m.ctrl.Call(m, "GetChatCostPerChat", ctx, arg)
+	ret0, _ := ret[0].([]database.GetChatCostPerChatRow)
+	ret1, _ := ret[1].(error)
+	return ret0, ret1
+}
+
+// GetChatCostPerChat indicates an expected call of GetChatCostPerChat.
+func (mr *MockStoreMockRecorder) GetChatCostPerChat(ctx, arg any) *gomock.Call {
+	mr.mock.ctrl.T.Helper()
+	return mr.mock.ctrl.RecordCallWithMethodType(mr.mock, "GetChatCostPerChat", reflect.TypeOf((*MockStore)(nil).GetChatCostPerChat), ctx, arg)
+}
+
+// GetChatCostPerModel mocks base method.
+func (m *MockStore) GetChatCostPerModel(ctx context.Context, arg database.GetChatCostPerModelParams) ([]database.GetChatCostPerModelRow, error) {
+	m.ctrl.T.Helper()
+	ret := m.ctrl.Call(m, "GetChatCostPerModel", ctx, arg)
+	ret0, _ := ret[0].([]database.GetChatCostPerModelRow)
+	ret1, _ := ret[1].(error)
+	return ret0, ret1
+}
+
+// GetChatCostPerModel indicates an expected call of GetChatCostPerModel.
+func (mr *MockStoreMockRecorder) GetChatCostPerModel(ctx, arg any) *gomock.Call {
+	mr.mock.ctrl.T.Helper()
+	return mr.mock.ctrl.RecordCallWithMethodType(mr.mock, "GetChatCostPerModel", reflect.TypeOf((*MockStore)(nil).GetChatCostPerModel), ctx, arg)
+}
+
+// GetChatCostPerUser mocks base method.
+func (m *MockStore) GetChatCostPerUser(ctx context.Context, arg database.GetChatCostPerUserParams) ([]database.GetChatCostPerUserRow, error) {
+	m.ctrl.T.Helper()
+	ret := m.ctrl.Call(m, "GetChatCostPerUser", ctx, arg)
+	ret0, _ := ret[0].([]database.GetChatCostPerUserRow)
+	ret1, _ := ret[1].(error)
+	return ret0, ret1
+}
+
+// GetChatCostPerUser indicates an expected call of GetChatCostPerUser.
+func (mr *MockStoreMockRecorder) GetChatCostPerUser(ctx, arg any) *gomock.Call {
+	mr.mock.ctrl.T.Helper()
+	return mr.mock.ctrl.RecordCallWithMethodType(mr.mock, "GetChatCostPerUser", reflect.TypeOf((*MockStore)(nil).GetChatCostPerUser), ctx, arg)
+}
+
+// GetChatCostSummary mocks base method.
+func (m *MockStore) GetChatCostSummary(ctx context.Context, arg database.GetChatCostSummaryParams) (database.GetChatCostSummaryRow, error) {
+	m.ctrl.T.Helper()
+	ret := m.ctrl.Call(m, "GetChatCostSummary", ctx, arg)
+	ret0, _ := ret[0].(database.GetChatCostSummaryRow)
+	ret1, _ := ret[1].(error)
+	return ret0, ret1
+}
+
+// GetChatCostSummary indicates an expected call of GetChatCostSummary.
+func (mr *MockStoreMockRecorder) GetChatCostSummary(ctx, arg any) *gomock.Call {
+	mr.mock.ctrl.T.Helper()
+	return mr.mock.ctrl.RecordCallWithMethodType(mr.mock, "GetChatCostSummary", reflect.TypeOf((*MockStore)(nil).GetChatCostSummary), ctx, arg)
+}
+
 // GetChatDiffStatusByChatID mocks base method.
 func (m *MockStore) GetChatDiffStatusByChatID(ctx context.Context, chatID uuid.UUID) (database.ChatDiffStatus, error) {
 	m.ctrl.T.Helper()