If you like, you can give dash-mantine-components a try, Select.
You can customise the message for no results like this:
dmc.Select(data=["a", "b"], searchable=True, nothingFound="Nothing matches your query")
If you want to remove this message altogether, just pass empty string or None to nothingFound
prop.
dmc.Select(data=["a", "b"], searchable=True, nothingFound="")