TIL that, not only does the MagSafe Battery Pack get firmware updates, but there’s a new one to upgrade it from 5w charging to 7.5w:
In order to get 7.5W charging on the go, update your MagSafe Battery Pack to the latest firmware. The firmware update begins automatically after you attach your battery pack to your iPhone. The firmware update can take about one week.
To update the firmware using a Mac or iPad, plug one end of a Lightning to USB cable into the Lightning connector on your battery pack, and the other end into your Mac or iPad. The firmware update will take about 5 minutes.
You can check that the update is complete on your iPhone in Settings > General > About > MagSafe Battery Pack. The Firmware Version will be 2.7.
Update April 21, 2022
I tried this with my Mac, and even after leaving the pack connected to the Mac overnight, it was still not updated. I unplugged/plugged it a few times, to no avail. I tried it with the iPad, and it didn’t work the first time—this is one of those times where Apple’s tendency to make these things happen invisibly is a drag—but it did the second time, and now I have the right firmware.