Hi Gwen,
Sorry for the late reply. For the mentioned use-case, in addition to the solution suggested by Alexandre, a small add-on that I would suggest is to, add a custom style class to the DropdownSearch Widget (ExtendedClass). Define the style definition for the custom class, chaining the pre-defined class as shown below.
CSS Snippet
.custom_SD .choices__list--dropdown .choices__list {
max-height: 200px;
}

Hope this helps you!
Kind regards,
Benjith Sam