docs(docs-infra): add search via queryparam all adev routes (#57567)

add search via a queryparam (?search=query) on all adev routes

PR Close #57567

adev/src/app/main.component.ts

@@ -0,0 +1,28 @@
+import {Component, effect, inject, model, WritableSignal} from '@angular/core';
+import {IS_SEARCH_DIALOG_OPEN, Search} from '@angular/docs';
+import {RouterOutlet} from '@angular/router';
+
+@Component({
+  standalone: true,
+  selector: 'adev-main',
+  imports: [RouterOutlet],
+  template: `<router-outlet />`,
+})
+export default class MainComponent {
+  private readonly displaySearchDialog: WritableSignal<boolean> = inject(IS_SEARCH_DIALOG_OPEN);
+  private readonly searchService = inject(Search);
+  search = model<string | undefined>('');
+
+  constructor() {
+    effect(
+      () => {
+        const search = this.search();
+        if (search !== undefined) {
+          this.displaySearchDialog.set(true);
+          this.searchService.updateSearchQuery(search);
+        }
+      },
+      {allowSignalWrites: true},
+    );
+  }
+}

adev/src/app/routes.ts

@@ -12,6 +12,7 @@ import {Route} from '@angular/router';
 import {DefaultPage, PagePrefix} from './core/enums/pages';
 import {SUB_NAVIGATION_DATA} from './sub-navigation-data';
 import {mapApiManifestToRoutes} from './features/references/helpers/manifest.helper';
+import MainComponent from './main.component';
 
 // Docs navigation data contains routes which navigates to /tutorials pages, in
 // that case we should load Tutorial component
@@ -236,6 +237,7 @@ const REDIRECT_ROUTES: Route[] = [
 export const routes: Route[] = [
   {
     path: '',
+    component: MainComponent,
     children: [
       {
         path: '',