Is there a way to combine switch and contains?

This works for your case

let photos: Set = ["jpg", "png", "tiff"]
let videos: Set = ["mp4", "mov", "mkv"]
let audios: Set = ["mp3", "wav", "wma"]

enum FileType {
    case photo, video, audio, unknown
}

func getType(of file: String) -> FileType {

   switch true {

   case photos.contains(file):
       return .photo
   case videos.contains(file):
       return .video
   case audios.contains(file):
       return .audio
   default:
       return .unknown
    }
}

print(getType(of: "mp4"))

video

You can switch on true and then use each case as the conditional when you have multiple conditions.

You can add an overload to the pattern-matching operator ~=:

func ~= <T> (pattern: Set<T>, value: T) -> Bool {
    return pattern.contains(value)
}

func getType(of file: String) -> FileType {
    switch file {
    case photos: return .photo
    case videos: return .video
    case audios: return .audio
    default: return .unknown
    }
}

I think your whole problem is the fact that you are trying to maintain 3 independent sets for every type instead of connecting them directly to a given file type:

enum FileType: String {
    case photo, video, audio, unknown
}

let extensions: [FileType: Set<String>] = [
    .photo: ["jpg", "png", "tiff"],
    .video: ["mp4", "mov", "mkv"],
    .audio: ["mp3", "wav", "wma"]
]

func getType(of file: String) -> FileType {
    return extensions.first { $0.value.contains(file) }?.key ?? .unknown
}