I found this article:
https://www.bannerbatterien.com/en-gb/Battery-knowledge/7-HOW-TO-Correctly-registering-start-stop-batteries
which advises whether registration is, or isn't necessary for a long list of vehicle manufacturers, unfortunately not including Subaru.
It does say, for example, for Audi "Without configuration or by installing a replacement battery from the free aftermarket, this may cause restrictions in the functionality and increased battery wear due to incorrectly functioning shut-off stages." For BMW, "Registration is required for all start-stop vehicles with IBS (intelligent battery sensor) from 2008 onwards. Without registration, the battery may be overcharged..."
They recommend using a memory saver, which plugs into the OBD socket and maintains a 12V supply while the old battery is replaced. They say "If a battery is replaced with the Memory Saver, it is usually not necessary to re-register." I tied wires to the positive and negative clamps, connected to a jump starter while I replaced my battery, which maintained power to the ECU and my car is showing no ill effects.
Somewhere else, I heard that, as a battery ages, the car's BEM charges it more aggressively, so not registering a new battery would cause it to be charged too aggressively and shorten its life, something that would pass unnoticed until it fails sooner than it should.
Can anyone confirm this?