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

site/src/api/typesGenerated.ts

@@ -1503,6 +1503,12 @@ export interface Chat {
 	 * attach or agent change.
 	 */
 	readonly last_injected_context?: readonly ChatMessagePart[];
+	/**
+	 * Context reports the chat's pinned workspace-context state and
+	 * whether it has drifted from the agent's latest pushed snapshot.
+	 * Nil when the chat has no pinned context yet.
+	 */
+	readonly context?: ChatContext;
 	readonly warnings?: readonly string[];
 	readonly client_type: ChatClientType;
 	/**
@@ -1587,6 +1593,29 @@ export interface ChatConfig {
 	readonly ai_gateway_routing_enabled: boolean;
 }
 
+// From codersdk/chats.go
+/**
+ * ChatContext reports a chat's pinned workspace context and whether it has
+ * drifted from the agent's latest pushed snapshot. The chat stays usable
+ * when dirty; refreshing re-pins it to the latest snapshot.
+ */
+export interface ChatContext {
+	/**
+	 * Dirty is true when the agent's latest snapshot hash differs from the
+	 * chat's pinned hash.
+	 */
+	readonly dirty: boolean;
+	/**
+	 * DirtySince is when drift was first detected; nil when not dirty.
+	 */
+	readonly dirty_since?: string;
+	/**
+	 * Error is the snapshot-level error copied from the pinned snapshot
+	 * (empty when healthy).
+	 */
+	readonly error?: string;
+}
+
 // From codersdk/chats.go
 export interface ChatContextFilePart {
 	readonly type: "context-file";
@@ -3037,6 +3066,7 @@ export interface ChatWatchEvent {
 // From codersdk/chats.go
 export type ChatWatchEventKind =
 	| "action_required"
+	| "context_dirty"
 	| "created"
 	| "deleted"
 	| "diff_status_change"
@@ -3046,6 +3076,7 @@ export type ChatWatchEventKind =
 
 export const ChatWatchEventKinds: ChatWatchEventKind[] = [
 	"action_required",
+	"context_dirty",
 	"created",
 	"deleted",
 	"diff_status_change",