Thanks for the replies stevemachine and IFIXH2O. I hadn't opened the cover to the pit before, and assumed that there was only one pump that the battery provided power to in the event of AC power failure.
But even if I had opened it up, I likely wouldn't have known that the black horn shaped thing seen in the attached picture was the backup pump. Thank you IFIX for educating me on that.
You probably can't tell from the picture, but the backup pump is pretty close to the top of the pit. Like I said, I didn't open the cover but I'm fairly certain I didn't fill the pit up that high when I tried to test the battery backup, which explains why it didn't kick in on its own or pump out any water when I pressed the "pump test" button.
As it stands, I'm going to monitor the pit if the power goes out to see if it kicks in and will have buckets at the ready in case it doesn't.
Much thanks to both of you, and keep an eye out for my next thread to be titled "I want to move my basement bathroom rough in"