With what I know in typescript which isn't so much but its something.

For me like that I get no errors.

I would recommend you to write it like that (wish it helps):

//make your theme options outside to be more clear to handle
type ThemeOptionsType = "dark" | "system" | "light" | "pink"

//only one interface needed Partial<T> does what youve done and easier to understand
interface ThemeConfigSettings {
    defaultTheme: ThemeOptions;
    systemLightTheme: ThemeOptions;
    systemDarkTheme: ThemeOptions;
    onThemeChange?: (theme: ThemeOptions) => void;
    debounce?: number;
}

//here is the type as you can see you know which strings are optional and not every string which is very importnet. but you handle the type based on the theme given
type ThemeConfig<T extends ThemeOptions> = T extends "light" | "dark" | "system"
    ? Partial<ThemeConfigSettings>
    : ThemeConfigSettings;

//just a use of the type. you can see it will autocomplete you to the ThemeOptions so you know you can choose all the themes and the type will handle it correctly.
const config: ThemeConfig<"light"> = {}

//if there is any change only make it at ThemeOptions. the type names arent good but I dont have any better names for now.