"What kind of costs are associated with having multiple applications?"
Short answer: that probably depends on your SLA. Without trying to speculate on your SLA the best thing to do would be to check with your customer success manager if this of concern
Generally speaking, when you create application copies you get a full copy of all the data that is backing the application. Production environments utilize Long Term Retention which is typically a Geo Redundant storage in the event some wild disaster happens. So these application copies will also get picked up by the LTR. That said, the raw Azure pricing for the geo redundant storage is just pennies per GB per month.
More details here:
https://docs.microsoft.com/en-us/azure/azure-sql/database/long-term-retention-overview?view=azuresql
https://azure.microsoft.com/en-us/pricing/details/storage/blobs/
But again, if you really want an answer, check with your customer success manager.
Cheers,
-db
