Progress is here for your business, like always. Read more about the measures we are taking to ensure business continuity and help fight the COVID-19 pandemic. Our thoughts here at Progress are with those affected by the outbreak.
Perhaps you could use an ItemTemplate and add a textbox in the first item where you could filter the data yourself, but I have not tested that and I am not sure how it would behave. Altering the data source may repaint the component and close the dropdown, so you may need to hook to some event or button there instead of using direct binding.
You may also want to vote and Follow the request for an AutoComplete component (https://feedback.telerik.com/blazor/1413657-autocomplete-component) as it will likely have a different UX - the dropdownlist would probably need you to expand it and focus a filter box in the dropdown, while the autocomplete would likely be a writeable input that shows a dropdown when you start typing.