"Has anyone heard of a stimulus payment for babies born in 2021?"

It's not "for babies born" but for all the people, for 2021, who qualify for the EIP or referred to as RRC, which is another Recovery stimulus advance payment. The tax return in 2020 was where you reconciled the first two EIP against qualifying data. The 2021 tax return is where you reconcile this Third round of payouts for that taxpayer, based on 2021 actuals. And it appears their household got a bit larger.