feat(coderd): add PR status summary to telemetry snapshots (#24379)

Adds aggregate PR counts (total, open, merged, closed) from
`chat_diff_statuses` to telemetry snapshots, giving visibility into AI
agent PR outcomes across deployments.

The existing telemetry system reports `Chats`, `ChatMessageSummaries`,
and `ChatModelConfigs`, but had no PR-level data. This adds a
`ChatDiffStatusSummary` field to the `Snapshot` struct with four
all-time counts derived from a single aggregate query.

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

- New SQL query `GetChatDiffStatusSummary` counts `chat_diff_statuses`
rows with non-NULL `pull_request_state`, grouped by state
(open/merged/closed).
- `ChatDiffStatusSummary` struct added to telemetry `Snapshot`,
collected via a parallel `eg.Go()` block in `createSnapshot()`.
- `dbauthz` wrapper uses `rbac.ResourceSystem` (telemetry-only pattern).
- Test covers both empty state (zero counts) and populated state (mixed
states + NULL-state exclusion).

</details>

> 🤖 Generated by Coder Agents

coderd/telemetry/telemetry.go

@@ -809,6 +809,19 @@ func (r *remoteReporter) createSnapshot() (*Snapshot, error) {
 		}
 		return nil
 	})
+	eg.Go(func() error {
+		row, err := r.options.Database.GetChatDiffStatusSummary(ctx)
+		if err != nil {
+			return xerrors.Errorf("get chat diff status summary: %w", err)
+		}
+		snapshot.ChatDiffStatusSummary = &ChatDiffStatusSummary{
+			Total:  row.Total,
+			Open:   row.Open,
+			Merged: row.Merged,
+			Closed: row.Closed,
+		}
+		return nil
+	})
 
 	err := eg.Wait()
 	if err != nil {
@@ -1540,6 +1553,7 @@ type Snapshot struct {
 	Chats                                []Chat                                `json:"chats"`
 	ChatMessageSummaries                 []ChatMessageSummary                  `json:"chat_message_summaries"`
 	ChatModelConfigs                     []ChatModelConfig                     `json:"chat_model_configs"`
+	ChatDiffStatusSummary                *ChatDiffStatusSummary                `json:"chat_diff_status_summary"`
 }
 
 // Deployment contains information about the host running Coder.
@@ -2173,6 +2187,9 @@ func ConvertChat(dbChat database.GetChatsUpdatedAfterRow) Chat {
 		c.Mode = &mode
 	}
 	c.ClientType = string(dbChat.ClientType)
+	if dbChat.PullRequestState.Valid {
+		c.PullRequestState = &dbChat.PullRequestState.String
+	}
 	return c
 }
 
@@ -2347,6 +2364,7 @@ type Chat struct {
 	Archived          bool       `json:"archived"`
 	LastModelConfigID uuid.UUID  `json:"last_model_config_id"`
 	ClientType        string     `json:"client_type"`
+	PullRequestState  *string    `json:"pull_request_state"`
 }
 
 // ChatMessageSummary contains per-chat aggregated message metrics
@@ -2380,6 +2398,17 @@ type ChatModelConfig struct {
 	IsDefault    bool      `json:"is_default"`
 }
 
+// ChatDiffStatusSummary contains aggregate PR counts across all
+// agent chats. Total counts unique PRs with a known state
+// (open + merged + closed). Open, Merged, and Closed break that
+// total down by state.
+type ChatDiffStatusSummary struct {
+	Total  int64 `json:"total"`
+	Open   int64 `json:"open"`
+	Merged int64 `json:"merged"`
+	Closed int64 `json:"closed"`
+}
+
 func ConvertAIBridgeInterceptionsSummary(endTime time.Time, provider, model, client string, summary database.CalculateAIBridgeInterceptionsTelemetrySummaryRow) AIBridgeInterceptionsSummary {
 	return AIBridgeInterceptionsSummary{
 		ID:                uuid.New(),