test: [UIE-10395 & UIE-10444] - Fix Parent/Child account switching bugs and test failures (#13470)

* Fix bug preventing child accounts from being fetched when signed in as a proxy user

* Work around debounce issue when searching for child accounts in test

* Added changeset: Fix test flakiness in account switching spec

Author: jdamore-linode

packages/manager/.changeset/pr-13470-tests-1772743282866.md

@@ -0,0 +1,5 @@
+---
+"@linode/manager": Tests
+---
+
+Fix test flakiness in account switching spec ([#13470](https://github.com/linode/manager/pull/13470))

packages/manager/cypress/e2e/core/parentChild/account-switching.spec.ts

@@ -366,7 +366,7 @@ describe('Parent/Child account switching', () => {
           // Confirm no results message.
           mockGetChildAccounts([]).as('getEmptySearchResults');
           cy.findByPlaceholderText('Search').click();
-          cy.focused().type('Fake Name');
+          cy.focused().type('Fake Name', { delay: 50 });
           cy.wait('@getEmptySearchResults');
 
           cy.contains(mockChildAccount.company).should('not.exist');
@@ -378,7 +378,7 @@ describe('Parent/Child account switching', () => {
           mockGetChildAccounts([mockChildAccount]).as('getSearchResults');
           cy.findByPlaceholderText('Search').click();
           cy.focused().clear();
-          cy.focused().type(mockChildAccount.company);
+          cy.focused().type(mockChildAccount.company, { delay: 50 });
           cy.wait('@getSearchResults');
 
           cy.findByText(mockChildAccount.company).should('be.visible');

packages/manager/src/features/Account/SwitchAccountDrawer.tsx

@@ -105,7 +105,7 @@ export const SwitchAccountDrawer = (props: Props) => {
           }
         : undefined,
     },
-    isIAMDelegationEnabled === false && isParentUserType
+    isIAMDelegationEnabled === false && (isParentUserType || isProxyUserType)
   );
 
   const {