Building a Search Bar to search custom post type

I’m trying to build a Searchbar to search movies. The search bar should get an inputtext that list the movie or list of movies. Movies is a custom post type. I also build the search functionalities that are in the twenty twenty theme but it only works with posts not for custom post type.

Ive read a lot in the community that I can build handlers or plugins like multiple cpt. I dont know exactly how to build the handler and the examples from some topic didnt help.

Is there maybe a new approach ?

Here my github repo: