TypeScript guard function for type-checking records by index signatures

guard.ts

type Check<T> = {
    [K in keyof T]: K extends `dull.${string}` 
        ? T[K] extends string
            ? T[K]
            : never 
        : K extends `rich.${string}` 
        ? T[K]
        : never
}

function isRichAndDull<T extends Record<string, any>>(value: Check<T>): Check<T> {
    return value
}

const config = isRichAndDull({
    "dull.foo": "hello",
    "rich.foo": new Date(),
})

What I'm ultimately aiming for, though, is something like this:

const config: RichAndDullConfig = {
    "dull.foo": "hello",
    "rich.foo": new Date(),
}

interface RichAndDullConfig {
    // Dull keys, e.g. "dull.foo" and "dull.bar" may only have string values.
    [dullKey: `dull.${string}`]: string;
    
    // Rich keys, e.g. "rich.foo" and "rich.bar" may have any value.
    [richKey: `rich.${string}`]: any;
}

... However, it fails with: An index signature parameter type must be either 'string' or 'number'. in TypeScript 4.3.