feat: Add apps sidebar tab (#9342)

## Summary

<!-- One sentence describing what changed and why. -->

## Changes

- **What**: <!-- Core functionality added/modified -->
- **Breaking**: <!-- Any breaking changes (if none, remove this line)
-->
- **Dependencies**: <!-- New dependencies (if none, remove this line)
-->

## Review Focus

<!-- Critical design decisions or edge cases that need attention -->

<!-- If this PR fixes an issue, uncomment and update the line below -->
<!-- Fixes #ISSUE_NUMBER -->

## Screenshots (if applicable)

<img width="383" height="359" alt="image"
src="https://github.com/user-attachments/assets/47905196-9db6-4a57-8cf7-384d4d37d000"
/>

<img width="335" height="281" alt="image"
src="https://github.com/user-attachments/assets/843068f3-e895-4781-bf5f-e0eb86d3387c"
/>

┆Issue is synchronized with this [Notion
page](https://www.notion.so/PR-9342-feat-Add-apps-sidebar-tab-3176d73d3650812b822fc9cc3f17322e)
by [Unito](https://www.unito.io)

---------

Co-authored-by: github-actions <github-actions@github.com>

src/components/sidebar/tabs/AppsSidebarTab.vue

@@ -0,0 +1,48 @@
+<template>
+  <BaseWorkflowsSidebarTab
+    :title="$t('linearMode.appModeToolbar.apps')"
+    :filter="isAppWorkflow"
+    :label-transform="stripAppJsonSuffix"
+    hide-leaf-icon
+    :search-subject="$t('linearMode.appModeToolbar.apps')"
+    data-testid="apps-sidebar"
+  >
+    <template #alt-title>
+      <span
+        class="ml-2 flex items-center rounded-full bg-primary-background px-1.5 py-0.5 text-xxs uppercase text-base-foreground"
+      >
+        {{ $t('g.beta') }}
+      </span>
+    </template>
+    <template #empty-state>
+      <NoResultsPlaceholder
+        button-variant="secondary"
+        text-class="text-muted-foreground text-sm"
+        :message="$t('linearMode.appModeToolbar.appsEmptyMessage')"
+        :button-label="$t('linearMode.appModeToolbar.enterAppMode')"
+        @action="enterAppMode"
+      />
+    </template>
+  </BaseWorkflowsSidebarTab>
+</template>
+
+<script setup lang="ts">
+import NoResultsPlaceholder from '@/components/common/NoResultsPlaceholder.vue'
+import BaseWorkflowsSidebarTab from '@/components/sidebar/tabs/BaseWorkflowsSidebarTab.vue'
+import { useAppMode } from '@/composables/useAppMode'
+import type { ComfyWorkflow } from '@/platform/workflow/management/stores/workflowStore'
+
+const { setMode } = useAppMode()
+
+function isAppWorkflow(workflow: ComfyWorkflow): boolean {
+  return workflow.suffix === 'app.json'
+}
+
+function stripAppJsonSuffix(label: string): string {
+  return label.replace(/\.app\.json$/i, '')
+}
+
+function enterAppMode() {
+  setMode('app')
+}
+</script>