We are other end users who respond based on our observations and experiences. We do not speak for Apple. These are my observations and experience with using the US Apple battery service for iPads.
Tracking and Contact: When I've had a battery service done on an iPad, Apple sent me confirmation emails and each one had contact info at the bottom for asking questions. Your repair number (needed) is in the same email. The emails go to the email address associated wit your Apple Account/Apple ID.
Experience:
—The store is highly unlikely to be doing the battery service. For iPads, a battery service is that a centralized Apple repair/refurbishment facility inspects yours and, if only the battery is a problem, they send you a refurbished iPad of the same model and specs.
—What is in a rerfurbed iPads is discussed here: Learn more about each refurbished iPad. The only difference is that a service refurb has a 90-day warranty.
— I have an iPad that was a battery service replacement refurb. The iPad was perfect and is still very usable 5 years later, only retired because it can no longer run the latest iPadOS version.
Observations re timing:
— If you drop off the iPad at a Genius Bar, they will likely forward it to the centralized repair refurbishment center where the work is done. Then the center sends the replacement back to the Apple store. Using the store drop can add a day on each end.
— The refurbed center apparenlty does not recieve shipments on weekends. I dropped my iPad at a local UPS store as instructed by Apple on a Friday morning. The refurb center did not get it until Monday morning.
— If the iPad is personalized, Apple will reproduce the personalization on the replacement, but that adds several days.
— If an exact configuration match to your original is not immediately available, they may wait for one to come up from the refurbishment section that matches.