You can put it in a Menu with a custom label:

Menu {
    Picker("Color Type", selection: $colorStyle) {
        ForEach(ColorStyle.allCases) { style in
            Text(String(describing: style))
        }
    }
} label: {
    HStack(spacing: 5) {
        Text(colorStyle.description)
        Image(systemName: "chevron.up.chevron.down")
    }
}
.labelsHidden()
.border(.green)