ui: Stores architecture improvements (#26910)

* refactor: Stores barrel imports + SSR gates

* refactor: Drop agenticStore wrapper exports

* refactor: Drop chatStore wrapper exports

* refactor: Drop modelsStore wrapper exports

* refactor: Drop serverStore wrapper exports

* refactor: Drop unused mcpStore wrapper exports

* refactor: Drop mcpResourceStore wrapper exports

* refactor: Drop conversationsStore wrapper exports + move buildConversationTree to utils

* refactor: Drop settingsStore wrapper exports

* refactor: Drop unused toolsStore wrapper exports

* refactor: Fix lint errors from store wrapper removal

* fix: Missing change

* refactor: Cleanup

* refactor: Context Stats store

tools/ui/src/lib/hooks/use-processing-state.svelte.ts

@@ -1,5 +1,5 @@
 import { STATS_UNITS } from '$lib/constants';
-import { activeProcessingState } from '$lib/stores/chat.svelte';
+import { chatStore } from '$lib/stores';
 import type { ApiProcessingState, LiveGenerationStats, LiveProcessingStats } from '$lib/types';
 
 export interface UseProcessingStateReturn {
@@ -42,8 +42,8 @@ export function useProcessingState(): UseProcessingStateReturn {
 			return lastKnownState;
 		}
 
-		// Read directly from the reactive state export
-		return activeProcessingState();
+		// Read directly from the reactive state
+		return chatStore.activeProcessingState;
 	});
 
 	$effect(() => {