While some of the information here is helpful, I'd like to address the root of the asker's specific question.

It fails with

TypeError: _dayjs.default.extend is not a function

Unfortunately similar questions on here didn't help me. How could I mock both default dayjs but also extend?

The default export of dayjs is a function with properties attached. Your mock needs to follow the same pattern. The following pseudo-code is written to be library agnostic:

const dayjsMock = () => ({
  add: () => {...}
});

dayjsMock.extend = () => {};

You'll plug this dayjsMock object into your specific mocking library's function.