Nested MenuItem don't close when using keyboard to select

[Al0ngsy]

What you were expecting:
When using the arrow key to navigate on NestedMenuItem-List the popup menu close upon changing to the next NestedMenuItem and a new menu popup open.

What happened instead:
When using the arrow key to navigate up and down on the NestedMenuItem-List the nested menu popup of the previous selected one are still there and don't close by themselves and the new popup are rendered above the old ones.

Steps to reproduce:

• go to https://codesandbox.io/s/material-ui-nested-menu-item-example-b25j6?file=/src/App.tsx:209-221
• right click on the text to open menu
• pressing keydown several times

[ProfessorX737]

Here is a javascript solution:
mui/material-ui#11723 (comment)