How long does it take for the IRS to process a payment after the return was accepted?

We cannot answer that.   The IRS is severely backlogged and everything they do is taking longer than normal.   You need to watch your own bank account or credit card to see when they process the payment.

When did you file?   If it's been a long time better double check your bank info.  And you know any tax due was due on May 15?   So you also might get a bill for interest.