You can limit the number of pickups per hour, per 15 minutes or per any other time interval of your choice.
Add the pickup time field to checkout
In order to achieve it please first add a Multiple Choice field in the checkout customizer.
You can add unlimited number of time slots. It can look like this:
The best position for the pickup time field is after pickup date.
Now please select this field as 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 pickup for a time interval option:
Once the pickups for the time slot for particular day will fill up the time slot will become unavailable.
Once all time slots for particular date will fill up the day will become unavailable.