It looks like it's possible to add css a limited amount of rules to the gmp-place-autocomplete selector.

Below is an example:

gmp-place-autocomplete {
    background-color: rgb(249 250 251);
    color-scheme: light;
    border: 1px solid rgb(209, 213, 219);
    border-radius: 9px;
}

See the documentation here
https://developers.google.com/maps/documentation/javascript/reference/places-widget#PlaceAutocompleteElement-CSS-Properties