webui: Conversation forking + branching improvements (#21021)

* refactor: Make `DialogConfirmation` extensible with children slot

* feat: Add conversation forking logic

* feat: Conversation forking UI

* feat: Update delete/edit dialogs and logic for forks

* refactor: Improve Chat Sidebar UX and add MCP Servers entry

* refactor: Cleanup

* feat: Update message in place when editing leaf nodes

* chore: Cleanup

* chore: Cleanup

* chore: Cleanup

* chore: Cleanup

* chore: Cleanup

* chore: Cleanup

* refactor: Post-review improvements

* chore: update webui build output

* test: Update Storybook test

* chore: update webui build output

* chore: update webui build output

tools/server/webui/tests/stories/ChatSidebar.stories.svelte

@@ -73,7 +73,7 @@
 			conversationsStore.conversations = mockConversations;
 		}, 0));
 		
-		const searchTrigger = screen.getByText('Search conversations');
+		const searchTrigger = screen.getByText('Search');
 		userEvent.click(searchTrigger);
 	}}
 >