[docs-infra] Tab navigation not working in `MuiProductSelector`

[alexfauquette]

Steps to reproduce

Open the product selector, and press tab to focus

You can use arrow up/down to move along the core producto, but you can not move to X or toolpad with keyboard because <Menu /> does prevent default on Tab press

Might need to rewrite it based on Popper, except if core team plan to support nested lists

Current behavior

No response

Expected behavior

No response

Context

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Your environment

npx @mui/envinfo

  Don't forget to mention which browser you used.
  Output from `npx @mui/envinfo` goes here.

Search keywords: menu docs-infra

[danilo-leal]

Good catch! The marketing pages' implementation of the menu is already using Popper, and it seems to suffer from a similar problem, too — you can't even focus the first chips on it. Have you noted that?