There are a variety of general platforms that could be used to this end.
Sure customizations may not be as diverse. But that is where you use a main site for internet visibility.
Apps like Line, WhatsApp, for example may allow phone calling.
A friend long ago did a delivery company on par with what your aiming for. With Restaurants, auto etc..
At that time it was someone chained to a desk answering the phone and using a CB somewhat closed system. He had tried before using Cell system CBs. But when he had a tower was much better.
These days people all pretty much have cell phones. So text systems for dispatching can work easy enough at low cost.
A good dispatcher is key. As they can organize things. Ie 2 restaurants with orders. If the restaurants are close to one another and the delivery destinations are near each other. A driver can pick up both orders.
When I dispatched for him. I would get the drivers to keep me informed where they are and move markers on a map. Restaurant taking calls can be quite grueling with high volume of calls.
Things like scheduled weekly deliveries is much better as 1 or 2 calls per client/week is easier to manage and yields better. 1 call the company makes more per call then say a restaurant where it is maybe a couple bucks for the company with a lot of work.
NOTE: Be careful if supporting debit to ensure you understand fees. The last time that friend setup a delivery company for restaurants & booze he ended up making nothing as the debit transactions between paying for orders and the fees charged for being able to accept debit payments.
Iirc at that time to accept debit was similar to a credit card where the company accepting pays a percentage of the sale ie 3%. So his $8 per delivery was greatly impacted by the total the end customer paid. So $100 order would cost say $3 decreasing his deliver charge to $5.