feat(site): add agent connection timings (#15276)

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<img width="1260" alt="Screenshot 2024-10-29 at 16 16 01"
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Close https://github.com/coder/internal/issues/116

---------

Co-authored-by: Danny Kopping <danny@coder.com>

coderd/apidoc/swagger.json

@@ -7992,6 +7992,28 @@
 				}
 			}
 		},
+		"codersdk.AgentConnectionTiming": {
+			"type": "object",
+			"properties": {
+				"ended_at": {
+					"type": "string",
+					"format": "date-time"
+				},
+				"stage": {
+					"$ref": "#/definitions/codersdk.TimingStage"
+				},
+				"started_at": {
+					"type": "string",
+					"format": "date-time"
+				},
+				"workspace_agent_id": {
+					"type": "string"
+				},
+				"workspace_agent_name": {
+					"type": "string"
+				}
+			}
+		},
 		"codersdk.AgentScriptTiming": {
 			"type": "object",
 			"properties": {
@@ -8006,7 +8028,7 @@
 					"type": "integer"
 				},
 				"stage": {
-					"type": "string"
+					"$ref": "#/definitions/codersdk.TimingStage"
 				},
 				"started_at": {
 					"type": "string",
@@ -8014,6 +8036,12 @@
 				},
 				"status": {
 					"type": "string"
+				},
+				"workspace_agent_id": {
+					"type": "string"
+				},
+				"workspace_agent_name": {
+					"type": "string"
 				}
 			}
 		},
@@ -10986,7 +11014,7 @@
 					"type": "string"
 				},
 				"stage": {
-					"type": "string"
+					"$ref": "#/definitions/codersdk.TimingStage"
 				},
 				"started_at": {
 					"type": "string",
@@ -12228,6 +12256,29 @@
 			"enum": ["UNSUPPORTED_WORKSPACES"],
 			"x-enum-varnames": ["TemplateVersionWarningUnsupportedWorkspaces"]
 		},
+		"codersdk.TimingStage": {
+			"type": "string",
+			"enum": [
+				"init",
+				"plan",
+				"graph",
+				"apply",
+				"start",
+				"stop",
+				"cron",
+				"connect"
+			],
+			"x-enum-varnames": [
+				"TimingStageInit",
+				"TimingStagePlan",
+				"TimingStageGraph",
+				"TimingStageApply",
+				"TimingStageStart",
+				"TimingStageStop",
+				"TimingStageCron",
+				"TimingStageConnect"
+			]
+		},
 		"codersdk.TokenConfig": {
 			"type": "object",
 			"properties": {
@@ -13475,7 +13526,14 @@
 		"codersdk.WorkspaceBuildTimings": {
 			"type": "object",
 			"properties": {
+				"agent_connection_timings": {
+					"type": "array",
+					"items": {
+						"$ref": "#/definitions/codersdk.AgentConnectionTiming"
+					}
+				},
 				"agent_script_timings": {
+					"description": "TODO: Consolidate agent-related timing metrics into a single struct when\nupdating the API version",
 					"type": "array",
 					"items": {
 						"$ref": "#/definitions/codersdk.AgentScriptTiming"