feat: add Prometheus metrics for chatd subsystem (#24371)

Adds 7 Prometheus metrics to the chatd subsystem and introduces typed
`ActivityBumpReason` for deadline bump attribution.

| Metric | Type | Labels |
|--------|------|--------|
| `coderd_chatd_chats` | Gauge | `state` (streaming, waiting) |
| `coderd_chatd_message_count` | Histogram | `provider` |
| `coderd_chatd_prompt_size_bytes` | Histogram | `provider` |
| `coderd_chatd_tool_result_size_bytes` | Histogram | `provider`,
`tool_name` |
| `coderd_chatd_ttft_seconds` | Histogram | `provider` |
| `coderd_chatd_compaction_total` | Counter | `provider`, `result` |
| `coderd_chatd_steps_total` | Counter | `provider` |

> 🤖

coderd/coderd.go

@@ -792,6 +792,7 @@ func New(options *Options) *API {
 			Pubsub:                         options.Pubsub,
 			WebpushDispatcher:              options.WebPushDispatcher,
 			UsageTracker:                   options.WorkspaceUsageTracker,
+			PrometheusRegistry:             options.PrometheusRegistry,
 		})
 		gitSyncLogger := options.Logger.Named("gitsync")
 		refresher := gitsync.NewRefresher(