I would like to share with you an amazing component library called React Aria.

React Aria is not a UI library, it's an unstyled component library by Adobe. It's accessibility-first, internationalized, functionality-included, interactive library of utility components.

One component that React Aria includes is the Autocomplete component. It includes a keyboard-controllable dropdown and a text input. It's currently in rc (Release Candidate), so if you're not looking to be ready for production too soon, it should be suitable for your needs. Do check it out!

If you'd like to implement the functionality you requested in your question yourself, you can see my other answer.