WHY AM I NOT SEEING THE FACEBOOK WIDGET OR SNAPCHAT WIDGET WHEN I TRY TO ADD TO MY LOCK SCREEN?

Not all apps/widgets can be added to the locked screen. It’s at the discretion of the app developer. Facebook appears as a choice on my iPhone but like you, it does not show up on my locked screen after adding. You can contact Apple Support but my guess it that’s it’s a Facebook issue.

Facebook shows up for me. I can add one of the 3 available widgets.

But tapping on them from the Lock Screen, fails after opening Facebook with a GraphQL Error if I try to use the large "Top Updates" option.

Not sure about Snapchat though.

When I first updated to ios16 the FB widget was showing as available for the lock screen but it’s since disappeared and I can’t work out how to get it back. Any ideas?