Depending on whether they have the battery in stock, whether the Geek who does battery replacements is working, and whether it can be scheduled, BB can replace the same day. I just had an iPhone XR battery replaced at BB. They didn't have the battery in stock so I had to wait 3 days... which turned into 10 days because they damaged the iPhone XR display and replaced the device w/ a new (possibly refurb) iPhone XR.. which was eligible for AC+. Figured I'd go for the monthly AC+ for the next year in the event my son damages the phone.
I didn't know with BB, thanks. I went to them for a battery replacement, but Apple wouldn't allow them to replace it because it was for a 6 Plus.
My only experience with Apple not replacing same day was mid-2017 I think. By that point, Apple was shipping the iPhone 5 to their main repair center and simply replacing the phone. So, had to wait for them to get the phone in.
As to your XR, Apple would tell you that it's 'remanufactured'. New casing, new battery and any parts failing QC replaced.