Is it pointless to let the same AI write the code and the tests?

Not a dumb question, it's the right worry. The tests protect against future changes breaking current behavior, which is still very valuable. They do not prove the current behavior is correct. That part has to come from you.

Cheap ways to add yourself into the loop:

• Write the test names yourself, in plain words: "invoice total includes 21% VAT", "credit note makes total negative". Let the AI fill in the code.
• Put real numbers from a real invoice you checked by hand into a test.
• Break the code on purpose (change 21 to 12). If no test fails, that rule isn't tested.

Also: a second, separate session reviewing the tests is better than nothing. "Here are the requirements [paste], here are the tests. Which requirements are not tested?" It doesn't share the first session's assumptions, so it catches some of them. Not a replacement for your own examples though.

Late, but to add: the term for Marco's third point is mutation testing, and there are tools that do it automatically (Stryker for JS/TS). They change your code in small ways and report which changes no test noticed. It's slow, so run it once in a while, not on every commit.