feat(coderd): add telemetry for agents chats and messages (#24068)

Adds telemetry collection for the agents chat system (`/agents`) to the
existing telemetry snapshot pipeline.

Three new snapshot fields:
- **`Chats`** — per-chat metadata (id, owner, status, mode,
workspace_id, root_chat_id, has_parent, archived, model config)
collected time-windowed via `createdAfter`
- **`ChatMessageSummaries`** — per-chat aggregated message metrics
(counts by role, token sums by type, cost, runtime, model count,
compression count) collected time-windowed
- **`ChatModelConfigs`** — model configuration metadata (provider,
model, context limit, enabled, default) collected as full dump

No PII is included — titles, message content, and URLs are excluded at
the SQL level. Only structural metadata flows through telemetry.

<details><summary>Implementation plan</summary>

### SQL Queries (`coderd/database/queries/chats.sql`)
- `GetChatsCreatedAfter` — time-windowed chat metadata
- `GetChatMessageSummariesPerChat` — per-chat message aggregates via
`GROUP BY`
- `GetChatModelConfigsForTelemetry` — full dump of model configs

### Telemetry (`coderd/telemetry/telemetry.go`)
- `Chat`, `ChatMessageSummary`, `ChatModelConfig` structs
- `ConvertChat`, `ConvertChatMessageSummary`, `ConvertChatModelConfig`
conversion functions
- Three `eg.Go()` blocks in `createSnapshot()` following the existing
collection pattern

### Authorization (`coderd/database/dbauthz/dbauthz.go`)
- System-only access for all three queries via `rbac.ResourceSystem`

### Tests
- `TestChatsTelemetry` in `coderd/telemetry/telemetry_test.go` — creates
chats (root + child), messages with token/cost data, model configs;
verifies all snapshot fields
- dbauthz test entries for all three queries in
`coderd/database/dbauthz/dbauthz_test.go`

</details>

> 🤖 Generated by Coder Agents

coderd/telemetry/telemetry.go

@@ -776,6 +776,40 @@ func (r *remoteReporter) createSnapshot() (*Snapshot, error) {
 		return nil
 	})
 
+	eg.Go(func() error {
+		chats, err := r.options.Database.GetChatsUpdatedAfter(ctx, createdAfter)
+		if err != nil {
+			return xerrors.Errorf("get chats updated after: %w", err)
+		}
+		snapshot.Chats = make([]Chat, 0, len(chats))
+		for _, chat := range chats {
+			snapshot.Chats = append(snapshot.Chats, ConvertChat(chat))
+		}
+		return nil
+	})
+	eg.Go(func() error {
+		summaries, err := r.options.Database.GetChatMessageSummariesPerChat(ctx, createdAfter)
+		if err != nil {
+			return xerrors.Errorf("get chat message summaries: %w", err)
+		}
+		snapshot.ChatMessageSummaries = make([]ChatMessageSummary, 0, len(summaries))
+		for _, s := range summaries {
+			snapshot.ChatMessageSummaries = append(snapshot.ChatMessageSummaries, ConvertChatMessageSummary(s))
+		}
+		return nil
+	})
+	eg.Go(func() error {
+		configs, err := r.options.Database.GetChatModelConfigsForTelemetry(ctx)
+		if err != nil {
+			return xerrors.Errorf("get chat model configs: %w", err)
+		}
+		snapshot.ChatModelConfigs = make([]ChatModelConfig, 0, len(configs))
+		for _, c := range configs {
+			snapshot.ChatModelConfigs = append(snapshot.ChatModelConfigs, ConvertChatModelConfig(c))
+		}
+		return nil
+	})
+
 	err := eg.Wait()
 	if err != nil {
 		return nil, err
@@ -1503,6 +1537,9 @@ type Snapshot struct {
 	AIBridgeInterceptionsSummaries       []AIBridgeInterceptionsSummary        `json:"aibridge_interceptions_summaries"`
 	BoundaryUsageSummary                 *BoundaryUsageSummary                 `json:"boundary_usage_summary"`
 	FirstUserOnboarding                  *FirstUserOnboarding                  `json:"first_user_onboarding"`
+	Chats                                []Chat                                `json:"chats"`
+	ChatMessageSummaries                 []ChatMessageSummary                  `json:"chat_message_summaries"`
+	ChatModelConfigs                     []ChatModelConfig                     `json:"chat_model_configs"`
 }
 
 // Deployment contains information about the host running Coder.
@@ -2113,6 +2150,66 @@ func ConvertTask(task database.Task) Task {
 	return t
 }
 
+// ConvertChat converts a database chat row to a telemetry Chat.
+func ConvertChat(dbChat database.GetChatsUpdatedAfterRow) Chat {
+	c := Chat{
+		ID:                dbChat.ID,
+		OwnerID:           dbChat.OwnerID,
+		CreatedAt:         dbChat.CreatedAt,
+		UpdatedAt:         dbChat.UpdatedAt,
+		Status:            string(dbChat.Status),
+		HasParent:         dbChat.HasParent,
+		Archived:          dbChat.Archived,
+		LastModelConfigID: dbChat.LastModelConfigID,
+	}
+	if dbChat.RootChatID.Valid {
+		c.RootChatID = &dbChat.RootChatID.UUID
+	}
+	if dbChat.WorkspaceID.Valid {
+		c.WorkspaceID = &dbChat.WorkspaceID.UUID
+	}
+	if dbChat.Mode.Valid {
+		mode := string(dbChat.Mode.ChatMode)
+		c.Mode = &mode
+	}
+	return c
+}
+
+// ConvertChatMessageSummary converts a database chat message
+// summary row to a telemetry ChatMessageSummary.
+func ConvertChatMessageSummary(dbRow database.GetChatMessageSummariesPerChatRow) ChatMessageSummary {
+	return ChatMessageSummary{
+		ChatID:                   dbRow.ChatID,
+		MessageCount:             dbRow.MessageCount,
+		UserMessageCount:         dbRow.UserMessageCount,
+		AssistantMessageCount:    dbRow.AssistantMessageCount,
+		ToolMessageCount:         dbRow.ToolMessageCount,
+		SystemMessageCount:       dbRow.SystemMessageCount,
+		TotalInputTokens:         dbRow.TotalInputTokens,
+		TotalOutputTokens:        dbRow.TotalOutputTokens,
+		TotalReasoningTokens:     dbRow.TotalReasoningTokens,
+		TotalCacheCreationTokens: dbRow.TotalCacheCreationTokens,
+		TotalCacheReadTokens:     dbRow.TotalCacheReadTokens,
+		TotalCostMicros:          dbRow.TotalCostMicros,
+		TotalRuntimeMs:           dbRow.TotalRuntimeMs,
+		DistinctModelCount:       dbRow.DistinctModelCount,
+		CompressedMessageCount:   dbRow.CompressedMessageCount,
+	}
+}
+
+// ConvertChatModelConfig converts a database model config row to a
+// telemetry ChatModelConfig.
+func ConvertChatModelConfig(dbRow database.GetChatModelConfigsForTelemetryRow) ChatModelConfig {
+	return ChatModelConfig{
+		ID:           dbRow.ID,
+		Provider:     dbRow.Provider,
+		Model:        dbRow.Model,
+		ContextLimit: dbRow.ContextLimit,
+		Enabled:      dbRow.Enabled,
+		IsDefault:    dbRow.IsDefault,
+	}
+}
+
 type telemetryItemKey string
 
 // The comment below gets rid of the warning that the name "TelemetryItemKey" has
@@ -2234,6 +2331,53 @@ type BoundaryUsageSummary struct {
 	PeriodDurationMilliseconds int64 `json:"period_duration_ms"`
 }
 
+// Chat contains anonymized metadata about a chat for telemetry.
+// Titles and message content are excluded to avoid PII leakage.
+type Chat struct {
+	ID                uuid.UUID  `json:"id"`
+	OwnerID           uuid.UUID  `json:"owner_id"`
+	CreatedAt         time.Time  `json:"created_at"`
+	UpdatedAt         time.Time  `json:"updated_at"`
+	Status            string     `json:"status"`
+	HasParent         bool       `json:"has_parent"`
+	RootChatID        *uuid.UUID `json:"root_chat_id"`
+	WorkspaceID       *uuid.UUID `json:"workspace_id"`
+	Mode              *string    `json:"mode"`
+	Archived          bool       `json:"archived"`
+	LastModelConfigID uuid.UUID  `json:"last_model_config_id"`
+}
+
+// ChatMessageSummary contains per-chat aggregated message metrics
+// for telemetry. Individual message content is never included.
+type ChatMessageSummary struct {
+	ChatID                   uuid.UUID `json:"chat_id"`
+	MessageCount             int64     `json:"message_count"`
+	UserMessageCount         int64     `json:"user_message_count"`
+	AssistantMessageCount    int64     `json:"assistant_message_count"`
+	ToolMessageCount         int64     `json:"tool_message_count"`
+	SystemMessageCount       int64     `json:"system_message_count"`
+	TotalInputTokens         int64     `json:"total_input_tokens"`
+	TotalOutputTokens        int64     `json:"total_output_tokens"`
+	TotalReasoningTokens     int64     `json:"total_reasoning_tokens"`
+	TotalCacheCreationTokens int64     `json:"total_cache_creation_tokens"`
+	TotalCacheReadTokens     int64     `json:"total_cache_read_tokens"`
+	TotalCostMicros          int64     `json:"total_cost_micros"`
+	TotalRuntimeMs           int64     `json:"total_runtime_ms"`
+	DistinctModelCount       int64     `json:"distinct_model_count"`
+	CompressedMessageCount   int64     `json:"compressed_message_count"`
+}
+
+// ChatModelConfig contains model configuration metadata for
+// telemetry. Sensitive fields like API keys are excluded.
+type ChatModelConfig struct {
+	ID           uuid.UUID `json:"id"`
+	Provider     string    `json:"provider"`
+	Model        string    `json:"model"`
+	ContextLimit int64     `json:"context_limit"`
+	Enabled      bool      `json:"enabled"`
+	IsDefault    bool      `json:"is_default"`
+}
+
 func ConvertAIBridgeInterceptionsSummary(endTime time.Time, provider, model, client string, summary database.CalculateAIBridgeInterceptionsTelemetrySummaryRow) AIBridgeInterceptionsSummary {
 	return AIBridgeInterceptionsSummary{
 		ID:                uuid.New(),