[web] Check adminPrivilegeAvailable to show "Project URL lookup" (#29020)

* Check `adminPrivilegeAvailable` to show "Project URL lookup"

This is the correct check as it's what used to decide if the AdminPanelRouter should be included:
ffa200d595/services/web/modules/admin-panel/index.mjs (L14-L15)

* Add "it displays expected admin menu items" to e2e tests

* Don't expect "Project URL lookup" in CE

* Revert "Don't expect "Project URL lookup" in CE"

This reverts commit 467cccbf6c0d538c386d459403c521e3f62cfee2.

* Make "Project URL Lookup" capitalization consistent

GitOrigin-RevId: ed5c219e9b5912a4c324cf9dce58061b58d911b0

server-ce/test/admin.spec.ts

@@ -135,6 +135,24 @@ describe('admin panel', function () {
       )
     })
 
+    describe('admin menu items', () => {
+      beforeEach(() => {
+        login(admin)
+        cy.visit('/project')
+      })
+
+      it('displays expected admin menu items', () => {
+        const menuitems = ['Manage Site', 'Manage Users', 'Project URL Lookup']
+        menuitems.forEach(name => {
+          cy.findByRole('menuitem', { name: 'Admin' }).click()
+          cy.get('ul[role="menu"]')
+            .findAllByRole('menuitem')
+            .should('have.length', menuitems.length)
+          cy.get('ul[role="menu"]').findByRole('menuitem', { name }).click()
+        })
+      })
+    })
+
     describe('manage site', () => {
       beforeEach(() => {
         login(admin)