You can limit the number of pickups per hour, per 15 minutes, or any other time interval.
Add the pickup time field to the checkout.
Please first add a Multiple Choice field in the checkout customizer to achieve it. You can add an unlimited number of time slots. It can look like this:
The best position for the pickup time field is below the pickup date.
Now please select this field as the pickup time field in Catalog > Settings > Shipping > Order Pickup:
Set the maximum number of pickups per time slot
To limit the number of pickups per time slot, please go to Catalog > Settings > Shipping > Order Pickup and set the number in the Max number of pickups for a time interval option:
Once the pickups for the time slot for a particular day will fill up, the time slot will become unavailable.
Once all time slots for a particular date fill up, the day will become unavailable.