You should not overwrite css in MUI's theme file, the problem you encounter is because many MUI components use the MuiList component (There are many basic components that are reused in complex components such as Drawer, Table, ...).
You also cannot css through class from sx or makeStyles because the dropdown of select is not a child component inside the root select but it creates a node outside the body tag (equal to the root if using react).
There are 2 ways to handle droppdown styles: