No additional steps required, you can return to your regularly scheduled gameplay.
Pressing the power button in once may not do anything when your Switch is frozen, but there's a hardware reboot in that power button that will work no matter what.
Not a fun time, especially if you're trying to get in a few minutes of game time on your work break.
That said, the message is clear, when updating your Wii U don't get impatient and unplug the system in the hope of starting again; you should also hope that your internet doesn't go down, either.
The high-profile case that's sparked the tales of woe came from Ben Fritz, film business reporter for the LA Times.
He was installing the hefty update (reportedly around 5GB, though that's not confirmed), wasn't convinced that it was still working due to the progress bar not moving and unplugged his machine to start again.
Click here for information on replacement and upgrade options.
Repairs for all other Nintendo 3DS family systems are still available. Be sure to include your SD card and any games that are having this issue with your repair.