[Vuejs]-How to correctly extend props?

The problem here is similar to another question, where only the validator property was a regular function. In your case, both validator and default are regular functions (albeit in different props), which inexplicably breaks the type inference for the props argument in setup(). I’m seeking the root problem in an open question.

Interestingly, your code creates this type for the props argument in setup(), which seems to be an intersection type of keys of string:

(parameter) props: Readonly<LooseRequired<Readonly<readonly unknown[] & {
    [x: number]: string;
} & {
    [Symbol.iterator]?: IterableIterator<string> | undefined;
    length?: number | undefined;
    toString?: string | undefined;
    toLocaleString?: string | undefined;
    ... 19 more ...;
    flat?: unknown[] | undefined;
}> | Readonly<...>>>

Workaround

Instead of regular functions, use arrow functions (when functions are needed) in all props declarations:

export default defineComponent({
  props: {
    when: {
      type: String,
      default: '',

      //validator(value: string) {
      //  return ['today', 'tomorrow', 'later'].includes(value)
      //},
      validator: (value: string) => ['today', 'tomorrow', 'later'].includes(value), // 

      required: true
    },
    data: {
      type: Object,

      //default() {
      //  return {}
      //},
      default: () => ({}), // 

      required: true
    },
  },
})

…which creates this type for the props argument:

(parameter) props: Readonly<LooseRequired<Readonly<{
    msg?: unknown;
    when?: unknown;
    data?: unknown;
} & {
    when: string;
    data: Record<string, any>;
} & {
    msg?: string | undefined;
}>>>

GitHub demo