not quite. today is 8/10 maybe it has if not by tomorrow Friday 8/11
If they are mailing your refund, then watch your mailbox. It may take about a week for the envelope to arrive in the mail. Open all mail even if it looks like junk mail.
"Your tax refund is scheduled to be mailed by August 11, 2023."
That means that your tax refund is scheduled to be mailed by tomorrow, August 11. It has not been mailed yet. A day or two after your refund has been mailed, the information on "Where's My Refund?" will be updated to say that it has been mailed.
When the IRS says they mailed a refund on a certain date, I think they really mean that they printed the check and put it in an envelope. It didn't necessarily get to the post office on that date. You should expect to receive the check a week or so after the IRS says they mailed it, but there's no fixed amount of time for mail to be delivered.