Recommenders for grad school applications have not submitted and deadline is imminent
You have done what you can, I think. Most likely it will turn out ok for two reasons.
First is that letters do tend to get written, even by procrastinators. And many professors are, indeed, procrastinators. But if you ping them three days in advance it is about all you can do.
Second is that the recipients also realize that professors are procrastinators and, being professors themselves will make some allowances in most (not all, alas) cases. The final decisions about things won't be made on the deadline dates and the staff will spend some time gathering things together for some future meeting. It is an easy task to add late arrivals.
They might not be so forgiving of the applicant as they are of each other, of course.
Relax for now. If it becomes a problem then the recipients will let you know an you will almost certainly get a chance to explain and correct it.