feat: integrate agent context snapshots into chats (#26389)

Makes the chat context foundation from #26385 live. That PR added the
storage columns, writer queries, and a dormant
`agentapi.ContextDirtyMarker` trigger with no production callers; this
PR wires them together end to end.

When a workspace agent pushes a context snapshot, bound chats now
hydrate to that snapshot's hash, and a later push with a different hash
flips already-pinned chats to dirty (emitting a `context_dirty` watch
event after the transaction commits). Chat creation pins the agent's
latest snapshot when one already exists. The experimental chat API
exposes this as `Chat.Context` (`*ChatContext` with `dirty`,
`dirty_since`, `error`), and a new `PUT
/api/experimental/chats/{chat}/context` endpoint re-pins the agent's
latest snapshot and clears the dirty marker.

`context_dirty_resources` stays NULL (the resource-level diff is
deferred to the UI phase) and the live per-turn context pull is
unchanged.

The end-to-end test provisions a workspace agent via the echo
provisioner, connects it over the Agent API v2.10, and exercises the
full path: an initial push hydrates a bound chat (clean), a second push
with a different hash marks it dirty, the API reports the dirty state,
and the refresh endpoint clears it.

<details>
<summary>Decision log</summary>

- **API shape — sub-struct.** Dirty state is surfaced as
`codersdk.Chat.Context *ChatContext { Dirty bool; DirtySince *time.Time;
Error string }` rather than flat fields, matching the RFC's named
`ChatContext` type and leaving room for future fields (resource diff,
sources). `db2sdk.Chat` populates it when the chat is context-tracked
(`len(ContextAggregateHash) > 0`), dirty, or carries a snapshot error,
and leaves it nil (`omitempty`) otherwise. `Dirty` mirrors
`context_dirty_since` being set.
- **Marker wiring.** The chat daemon is injected directly as the
`agentapi.ContextDirtyMarker`. It is unconditionally constructed (only
its background worker is gated), so the marker is always non-nil and the
wiring matches every other `api.chatDaemon` call site. `agentapi` still
treats a nil marker as "chatd absent", so `PushContextState` stays a
pure write path for any future caller that does not wire chatd in.
- **Refresh is atomic.** `RefreshChatContext` reads the agent's latest
snapshot and re-pins the chat in one repeatable-read transaction, so a
concurrent push cannot land between the read and the write and leave the
chat pinned to a stale hash with the dirty marker cleared.
- **Hydrate + dirty run inside the push transaction.** The fan-out
shares the push's transaction so a concurrent refresh cannot interleave
with the version gate; `context_dirty` watch events publish only after
commit. The pinned hash on dirtied chats is intentionally left unchanged
— the refresh endpoint re-pins it.
- **Dirtied chats keep their pinned hash.** Drift is advisory: a dirty
chat stays usable, and refreshing is the only path that advances the
pinned hash.
- **Test binds `chats.agent_id` directly.** In production the binding is
set lazily during a chat turn (`chatd.persistBuildAgentBinding`); the
test sets it via `dbgen` so it exercises the context flow rather than
turn resolution.

Plan: `coderd/x/chatd` context integration + E2E (sub-struct API,
create-time + push-time hydration, refresh endpoint;
`context_dirty_resources` and the per-turn pull untouched).

</details>

🤖 Generated by Coder Agents on behalf of @kylecarbs

coderd/apidoc/swagger.json

@@ -482,6 +482,38 @@
 				}
 			}
 		},
+		"/api/experimental/chats/{chat}/context": {
+			"put": {
+				"description": "Experimental: this endpoint is subject to change.",
+				"produces": ["application/json"],
+				"tags": ["Chats"],
+				"summary": "Refresh chat context",
+				"operationId": "refresh-chat-context",
+				"parameters": [
+					{
+						"type": "string",
+						"format": "uuid",
+						"description": "Chat ID",
+						"name": "chat",
+						"in": "path",
+						"required": true
+					}
+				],
+				"responses": {
+					"200": {
+						"description": "OK",
+						"schema": {
+							"$ref": "#/definitions/codersdk.Chat"
+						}
+					}
+				},
+				"security": [
+					{
+						"CoderSessionToken": []
+					}
+				]
+			}
+		},
 		"/api/experimental/chats/{chat}/diff": {
 			"get": {
 				"description": "Experimental: this endpoint is subject to change.",
@@ -14764,6 +14796,14 @@
 				"client_type": {
 					"$ref": "#/definitions/codersdk.ChatClientType"
 				},
+				"context": {
+					"description": "Context reports the chat's pinned workspace-context state and\nwhether it has drifted from the agent's latest pushed snapshot.\nNil when the chat has no pinned context yet.",
+					"allOf": [
+						{
+							"$ref": "#/definitions/codersdk.ChatContext"
+						}
+					]
+				},
 				"created_at": {
 					"type": "string",
 					"format": "date-time"
@@ -14907,6 +14947,24 @@
 				}
 			}
 		},
+		"codersdk.ChatContext": {
+			"type": "object",
+			"properties": {
+				"dirty": {
+					"description": "Dirty is true when the agent's latest snapshot hash differs from the\nchat's pinned hash.",
+					"type": "boolean"
+				},
+				"dirty_since": {
+					"description": "DirtySince is when drift was first detected; nil when not dirty.",
+					"type": "string",
+					"format": "date-time"
+				},
+				"error": {
+					"description": "Error is the snapshot-level error copied from the pinned snapshot\n(empty when healthy).",
+					"type": "string"
+				}
+			}
+		},
 		"codersdk.ChatDiffContents": {
 			"type": "object",
 			"properties": {
@@ -15816,7 +15874,8 @@
 				"created",
 				"deleted",
 				"diff_status_change",
-				"action_required"
+				"action_required",
+				"context_dirty"
 			],
 			"x-enum-varnames": [
 				"ChatWatchEventKindStatusChange",
@@ -15825,7 +15884,8 @@
 				"ChatWatchEventKindCreated",
 				"ChatWatchEventKindDeleted",
 				"ChatWatchEventKindDiffStatusChange",
-				"ChatWatchEventKindActionRequired"
+				"ChatWatchEventKindActionRequired",
+				"ChatWatchEventKindContextDirty"
 			]
 		},
 		"codersdk.ConnectionLatency": {