Quick answer: Once a refund is issued, it shows up on your statement within 5-10 business days. The exact timing is on your bank or card issuer's end.
Failed-payment holds are different
If you saw a charge from a payment that failed, that's a temporary authorization hold, not a refund. It reverses on its own within up to 10 business days. See "I was charged but got no confirmation."
When to reach out
A refund you were told was approved hasn't appeared after 10 business days.