Missing Notification Center Widgets & Share Extensions

Half of my Notification Center widgets (most importantly, Weather) suddenly disappeared, and can no longer be added back by clicking Edit at the bottom of the Notification Center. Those that remain, like Today and Tomorrow, show no information.

They are also missing from  → System Preferences → Extensions → Today.

I’ve tried reinstalling the macOS 10.12.3 Combo Update, with no success through multiple reboots.

Apple has a knowledge base article for this bug occasionally affecting macOS Yosemite, El Capitan, and now Sierra. This happens most often after installing an OS update.

To reregister all Notification Center widgets and Share Extensions, start a Terminal session, and enter the following:

/System/Library/Frameworks/CoreServices.framework/Versions/A/Frameworks/LaunchServices.framework/Versions/A/Support/lsregister -kill -seed

(Triple-click the above line and press ⌘ cmdc to copy, then ⌘ cmdv inside Terminal.)