[material-ui][Select] Cycle On Focus Without Having Options Open

Summary

When using the Select as a drop down, it would be nice to be able to cycle through the options by typing in the first letter of the options that you'd like to cycle through. Right now it's possible to do the cycle while the options are open, but once the options are closed, hitting the keys doesn't cycle it.

Examples

To test out the current behavior, you can go to https://mui.com/material-ui/react-select/#basic-select and click on the select to focus on it, then close the options selector. Then try and cycle through the options with the T key.

Here's Amazon's version of one that works as this issue states:
https://github.com/mui/material-ui/assets/10539109/81592f3e-81ed-44bf-97cf-b752e6711afa

I was cycling by just pressing the A key.

Motivation

This is a feature available on a lot of other libraries(see ChakraUI: https://v2.chakra-ui.com/docs/components/select) and just on the web in general so a similar feature on MUI would be nice.

Search keywords: cycle select

Start with the Material UI Select basic example linked in the issue and compare keyboard behavior while the options are open versus closed. Verify how typing the first letter currently cycles options, then confirm that the same behavior works while the Select remains focused after its menu closes.