Switch version 12.1.0 includes an update for the Joy-Con
As part of Switch version 12.1.0, it turns out that the Joy-Con can also be updated.
This can be done by accessing the system settings. Go to the “Controllers and Settings” tab and scroll down to “Update Controllers”. Joy-Con that are connected should then be updated. Unfortunately, Nintendo has never made it clear what the process actually does.
Switch version 12.1.0 dropped a short while ago. You can read about the system update here.
Thanks to Cameron and Bernardo N for the tip.