feat(chats): archive chats instead of hard-deleting them (#22406)

## Summary

The UI has always labeled the action as "Archive agent" but the backend
was performing a hard `DELETE`, permanently destroying chats and all
their messages.

This change replaces the hard delete with a soft archive, consistent
with the pattern used by template versions.

## Changes

### Database
- **Migration 000423**: Add `archived boolean DEFAULT false NOT NULL`
column to `chats` table
- Replace `DeleteChatByID` query with `ArchiveChatByID` (`UPDATE SET
archived = true`)
- Add `UnarchiveChatByID` query (`UPDATE SET archived = false`)
- Filter archived chats from `GetChatsByOwnerID` (`WHERE archived =
false`)

### API
- Remove `DELETE /api/experimental/chats/{chat}`
- Add `POST /api/experimental/chats/{chat}/archive` — archives a chat
and all its descendants
- Add `POST /api/experimental/chats/{chat}/unarchive` — unarchives a
single chat (API only, no UI yet)

### Backend
- `archiveChatTree()` recursively archives child chats (replaces
`deleteChatTree()` which hard-deleted)
- Chat daemon's `ArchiveChat()` archives the full chat tree in a
transaction
- Authorization uses `ActionUpdate` instead of `ActionDelete`

### SDK
- Replace `DeleteChat()` with `ArchiveChat()` and `UnarchiveChat()`
- Add `Archived` field to `Chat` struct

### Frontend
- `archiveChat` API call uses `POST .../archive` instead of `DELETE`
- No UI changes — the "Archive agent" button now actually archives
instead of deleting

## Design Decision

This follows the **template version archive pattern** (Pattern B in the
codebase):
- `archived boolean` column (not `deleted boolean`)
- Dedicated `POST .../archive` and `POST .../unarchive` routes (not
repurposing `DELETE`)
- Reversible — users can unarchive via the API (UI for this will come
later)

coderd/database/dbmock/dbmock.go

@@ -132,6 +132,20 @@ func (mr *MockStoreMockRecorder) AllUserIDs(ctx, includeSystem any) *gomock.Call
 	return mr.mock.ctrl.RecordCallWithMethodType(mr.mock, "AllUserIDs", reflect.TypeOf((*MockStore)(nil).AllUserIDs), ctx, includeSystem)
 }
 
+// ArchiveChatByID mocks base method.
+func (m *MockStore) ArchiveChatByID(ctx context.Context, id uuid.UUID) error {
+	m.ctrl.T.Helper()
+	ret := m.ctrl.Call(m, "ArchiveChatByID", ctx, id)
+	ret0, _ := ret[0].(error)
+	return ret0
+}
+
+// ArchiveChatByID indicates an expected call of ArchiveChatByID.
+func (mr *MockStoreMockRecorder) ArchiveChatByID(ctx, id any) *gomock.Call {
+	mr.mock.ctrl.T.Helper()
+	return mr.mock.ctrl.RecordCallWithMethodType(mr.mock, "ArchiveChatByID", reflect.TypeOf((*MockStore)(nil).ArchiveChatByID), ctx, id)
+}
+
 // ArchiveUnusedTemplateVersions mocks base method.
 func (m *MockStore) ArchiveUnusedTemplateVersions(ctx context.Context, arg database.ArchiveUnusedTemplateVersionsParams) ([]uuid.UUID, error) {
 	m.ctrl.T.Helper()
@@ -540,20 +554,6 @@ func (mr *MockStoreMockRecorder) DeleteApplicationConnectAPIKeysByUserID(ctx, us
 	return mr.mock.ctrl.RecordCallWithMethodType(mr.mock, "DeleteApplicationConnectAPIKeysByUserID", reflect.TypeOf((*MockStore)(nil).DeleteApplicationConnectAPIKeysByUserID), ctx, userID)
 }
 
-// DeleteChatByID mocks base method.
-func (m *MockStore) DeleteChatByID(ctx context.Context, id uuid.UUID) error {
-	m.ctrl.T.Helper()
-	ret := m.ctrl.Call(m, "DeleteChatByID", ctx, id)
-	ret0, _ := ret[0].(error)
-	return ret0
-}
-
-// DeleteChatByID indicates an expected call of DeleteChatByID.
-func (mr *MockStoreMockRecorder) DeleteChatByID(ctx, id any) *gomock.Call {
-	mr.mock.ctrl.T.Helper()
-	return mr.mock.ctrl.RecordCallWithMethodType(mr.mock, "DeleteChatByID", reflect.TypeOf((*MockStore)(nil).DeleteChatByID), ctx, id)
-}
-
 // DeleteChatMessagesAfterID mocks base method.
 func (m *MockStore) DeleteChatMessagesAfterID(ctx context.Context, arg database.DeleteChatMessagesAfterIDParams) error {
 	m.ctrl.T.Helper()
@@ -6901,6 +6901,20 @@ func (mr *MockStoreMockRecorder) TryAcquireLock(ctx, pgTryAdvisoryXactLock any)
 	return mr.mock.ctrl.RecordCallWithMethodType(mr.mock, "TryAcquireLock", reflect.TypeOf((*MockStore)(nil).TryAcquireLock), ctx, pgTryAdvisoryXactLock)
 }
 
+// UnarchiveChatByID mocks base method.
+func (m *MockStore) UnarchiveChatByID(ctx context.Context, id uuid.UUID) error {
+	m.ctrl.T.Helper()
+	ret := m.ctrl.Call(m, "UnarchiveChatByID", ctx, id)
+	ret0, _ := ret[0].(error)
+	return ret0
+}
+
+// UnarchiveChatByID indicates an expected call of UnarchiveChatByID.
+func (mr *MockStoreMockRecorder) UnarchiveChatByID(ctx, id any) *gomock.Call {
+	mr.mock.ctrl.T.Helper()
+	return mr.mock.ctrl.RecordCallWithMethodType(mr.mock, "UnarchiveChatByID", reflect.TypeOf((*MockStore)(nil).UnarchiveChatByID), ctx, id)
+}
+
 // UnarchiveTemplateVersion mocks base method.
 func (m *MockStore) UnarchiveTemplateVersion(ctx context.Context, arg database.UnarchiveTemplateVersionParams) error {
 	m.ctrl.T.Helper()