fix(agents): persist system prompt server-side instead of localStorage (#22857)

## Problem

The Admin → Agents → System Prompt textarea saved only to the browser's
`localStorage`. The value was never sent to the backend, never stored in
the database, and never injected into chats. Entering text, clicking
Save, and refreshing the page showed no changes — the prompt was
effectively a no-op.

## Root Cause

Three disconnected layers:
1. **Frontend** wrote to `localStorage`, never called an API.
2. **`handleCreateChat`** never read `savedSystemPrompt`.
3. **Backend** hardcoded `chatd.DefaultSystemPrompt` on every chat
creation — no field in `CreateChatRequest` accepted a custom prompt.

## Changes

### Database
- Added `GetChatSystemPrompt` / `UpsertChatSystemPrompt` queries on the
existing `site_configs` table (no migration needed).

### API
- `GET /api/experimental/chats/system-prompt` — returns the configured
prompt (any authenticated user).
- `PUT /api/experimental/chats/system-prompt` — sets the prompt
(admin-only, `rbac: deployment_config update`).
- Input validation: max 32 KiB prompt length.

### Backend
- `resolvedChatSystemPrompt(ctx)` checks for a custom prompt in the DB,
falls back to `chatd.DefaultSystemPrompt` when empty/unset.
- Logs a warning on DB errors instead of silently swallowing them.
- Replaced the hardcoded `defaultChatSystemPrompt()` call in chat
creation.

### Frontend
- Replaced `localStorage` read/write with React Query
`useQuery`/`useMutation` backed by the new endpoints.
- Fixed `useEffect` draft sync to avoid clobbering in-progress user
edits on refetch.
- Added `try/catch` error handling on save (draft stays dirty for
retry).
- Save button disabled during mutation (`isSavingSystemPrompt`).
- Query key follows kebab-case convention (`chat-system-prompt`).

### UX
- Added hint: "When empty, the built-in default prompt is used."

### Tests
- `TestChatSystemPrompt`: GET returns empty when unset, admin can set,
non-admin gets 403.
- dbauthz `TestMethodTestSuite` coverage for both new querier methods.

coderd/database/dbauthz/dbauthz.go

@@ -2564,6 +2564,18 @@ func (q *querier) GetChatQueuedMessages(ctx context.Context, chatID uuid.UUID) (
 	return q.db.GetChatQueuedMessages(ctx, chatID)
 }
 
+func (q *querier) GetChatSystemPrompt(ctx context.Context) (string, error) {
+	// The system prompt is a deployment-wide setting read during chat
+	// creation by every authenticated user, so no RBAC policy check
+	// is needed. We still verify that a valid actor exists in the
+	// context to ensure this is never callable by an unauthenticated
+	// or system-internal path without an explicit actor.
+	if _, ok := ActorFromContext(ctx); !ok {
+		return "", ErrNoActor
+	}
+	return q.db.GetChatSystemPrompt(ctx)
+}
+
 func (q *querier) GetChatsByOwnerID(ctx context.Context, ownerID database.GetChatsByOwnerIDParams) ([]database.Chat, error) {
 	return fetchWithPostFilter(q.auth, policy.ActionRead, q.db.GetChatsByOwnerID)(ctx, ownerID)
 }
@@ -6536,6 +6548,13 @@ func (q *querier) UpsertChatDiffStatusReference(ctx context.Context, arg databas
 	return q.db.UpsertChatDiffStatusReference(ctx, arg)
 }
 
+func (q *querier) UpsertChatSystemPrompt(ctx context.Context, value string) error {
+	if err := q.authorizeContext(ctx, policy.ActionUpdate, rbac.ResourceDeploymentConfig); err != nil {
+		return err
+	}
+	return q.db.UpsertChatSystemPrompt(ctx, value)
+}
+
 func (q *querier) UpsertConnectionLog(ctx context.Context, arg database.UpsertConnectionLogParams) (database.ConnectionLog, error) {
 	if err := q.authorizeContext(ctx, policy.ActionUpdate, rbac.ResourceConnectionLog); err != nil {
 		return database.ConnectionLog{}, err

coderd/database/dbauthz/dbauthz_test.go

@@ -551,6 +551,10 @@ func (s *MethodTestSuite) TestChats() {
 		dbm.EXPECT().GetChatQueuedMessages(gomock.Any(), chat.ID).Return(qms, nil).AnyTimes()
 		check.Args(chat.ID).Asserts(chat, policy.ActionRead).Returns(qms)
 	}))
+	s.Run("GetChatSystemPrompt", s.Mocked(func(dbm *dbmock.MockStore, _ *gofakeit.Faker, check *expects) {
+		dbm.EXPECT().GetChatSystemPrompt(gomock.Any()).Return("prompt", nil).AnyTimes()
+		check.Args().Asserts()
+	}))
 	s.Run("GetEnabledChatModelConfigs", s.Mocked(func(dbm *dbmock.MockStore, faker *gofakeit.Faker, check *expects) {
 		configA := testutil.Fake(s.T(), faker, database.ChatModelConfig{})
 		configB := testutil.Fake(s.T(), faker, database.ChatModelConfig{})
@@ -758,6 +762,10 @@ func (s *MethodTestSuite) TestChats() {
 		dbm.EXPECT().UpsertChatDiffStatusReference(gomock.Any(), arg).Return(diffStatus, nil).AnyTimes()
 		check.Args(arg).Asserts(chat, policy.ActionUpdate).Returns(diffStatus)
 	}))
+	s.Run("UpsertChatSystemPrompt", s.Mocked(func(dbm *dbmock.MockStore, _ *gofakeit.Faker, check *expects) {
+		dbm.EXPECT().UpsertChatSystemPrompt(gomock.Any(), "").Return(nil).AnyTimes()
+		check.Args("").Asserts(rbac.ResourceDeploymentConfig, policy.ActionUpdate)
+	}))
 }
 
 func (s *MethodTestSuite) TestFile() {