Ok, thank you for the responses. Somehow I felt like 50% of the combobox was already doone and the path with LIveview only felt pretty good. I do understand the snappyness of this kind of interface would suffer from a roundtrip to the server.
For full solution reference, I went the web-components route as described in this topic: Phoenix LiveView + HeadlessUI
Thanks to @fteschke and @superchris for the inspiration.