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/dbmock/dbmock.go

@@ -2017,6 +2017,21 @@ func (mr *MockStoreMockRecorder) GetChatQueuedMessages(ctx, chatID any) *gomock.
 	return mr.mock.ctrl.RecordCallWithMethodType(mr.mock, "GetChatQueuedMessages", reflect.TypeOf((*MockStore)(nil).GetChatQueuedMessages), ctx, chatID)
 }
 
+// GetChatSystemPrompt mocks base method.
+func (m *MockStore) GetChatSystemPrompt(ctx context.Context) (string, error) {
+	m.ctrl.T.Helper()
+	ret := m.ctrl.Call(m, "GetChatSystemPrompt", ctx)
+	ret0, _ := ret[0].(string)
+	ret1, _ := ret[1].(error)
+	return ret0, ret1
+}
+
+// GetChatSystemPrompt indicates an expected call of GetChatSystemPrompt.
+func (mr *MockStoreMockRecorder) GetChatSystemPrompt(ctx any) *gomock.Call {
+	mr.mock.ctrl.T.Helper()
+	return mr.mock.ctrl.RecordCallWithMethodType(mr.mock, "GetChatSystemPrompt", reflect.TypeOf((*MockStore)(nil).GetChatSystemPrompt), ctx)
+}
+
 // GetChatsByOwnerID mocks base method.
 func (m *MockStore) GetChatsByOwnerID(ctx context.Context, arg database.GetChatsByOwnerIDParams) ([]database.Chat, error) {
 	m.ctrl.T.Helper()
@@ -8463,6 +8478,20 @@ func (mr *MockStoreMockRecorder) UpsertChatDiffStatusReference(ctx, arg any) *go
 	return mr.mock.ctrl.RecordCallWithMethodType(mr.mock, "UpsertChatDiffStatusReference", reflect.TypeOf((*MockStore)(nil).UpsertChatDiffStatusReference), ctx, arg)
 }
 
+// UpsertChatSystemPrompt mocks base method.
+func (m *MockStore) UpsertChatSystemPrompt(ctx context.Context, value string) error {
+	m.ctrl.T.Helper()
+	ret := m.ctrl.Call(m, "UpsertChatSystemPrompt", ctx, value)
+	ret0, _ := ret[0].(error)
+	return ret0
+}
+
+// UpsertChatSystemPrompt indicates an expected call of UpsertChatSystemPrompt.
+func (mr *MockStoreMockRecorder) UpsertChatSystemPrompt(ctx, value any) *gomock.Call {
+	mr.mock.ctrl.T.Helper()
+	return mr.mock.ctrl.RecordCallWithMethodType(mr.mock, "UpsertChatSystemPrompt", reflect.TypeOf((*MockStore)(nil).UpsertChatSystemPrompt), ctx, value)
+}
+
 // UpsertConnectionLog mocks base method.
 func (m *MockStore) UpsertConnectionLog(ctx context.Context, arg database.UpsertConnectionLogParams) (database.ConnectionLog, error) {
 	m.ctrl.T.Helper()