"I tried "Where's My Refund" on the IRS website, but it just said that the return was still being processed. I don't believe this"

Why not? That's why they provide that portal.

And if the amount was sent to that bank account which had an Overdraft condition, the bank would hold that against collection:

https://www.moneycrashers.com/reasons-irs-seize-tax-refund-money-debt/