Remove null attributes from an Object in Typescript

As reference Remove blank attributes from an Object in Javascript, how to make it Typescript compatible?

JS function (nested objects | ES10):

function removeEmpty(obj) {
  return Object.fromEntries(
    Object.entries(obj)
      .filter(([_, v]) => v != null)
      .map(([k, v]) => [k, v === Object(v) ? removeEmpty(v) : v])
  );
}

I've tried with Exclude<T, null> but it doesn't works with nested objects and I think it's not the correct utility to use.

Note that the returned type should remove null type(s) but keeps undefined.

Example/Expected behaviour:

type TestType = {
  a?: {
    b?: {
      c: string;
    } | null;
    z?: {
      x: string;
    };
  } | null;
};

const testObj: TestType = {
  a: {
    b: null,
    z: { x: 'Hi' }
  }
};

const resultObj = removeEmpty(testObj);

Where resultObj type is similar to:

type ResultTestTypeExample = {
  a?: {
    b?: {
      c: string;
    };
    z?: {
      x: string;
    };
  };
};

Does this work for you?

type ExpandRecursively<T> = T extends object
  ? T extends infer O ? { [K in keyof O]: ExpandRecursively<O[K]> } : never
  : T;

type RemoveNull<T> = ExpandRecursively<{ [K in keyof T]: Exclude<RemoveNull<T[K]>, null> }>

Usage:

function removeEmpty<T>(obj: T): RemoveNull<T> {
  return Object.fromEntries(
    Object.entries(obj)
      .filter(([_, v]) => v != null)
      .map(([k, v]) => [k, v === Object(v) ? removeEmpty(v) : v])
  ) as RemoveNull<T>
}

Playground