Hey there, friends!
Found a fix that worked for me...
For those of you who are tech-savvy, I just signed out of iCloud and then back into it (on my Mac). This is a slightly arduous process because it requires you to download your iCloud information to your Mac... It took a total of about 15 minutes, but now everything is working just fine (as it relates to Continuity Camera)!
- Go to System preferences
- Select iCloud (3rd row down, first one on the left)
-Select "Sign Out"
-I would recommend selecting "Keep a Copy"
-It will download a copy of your iCloud content not stored on your Mac.
-After the process has finished and it has signed you out (it may prompt you for a few more things in the process), RESTART your Mac. Just a normal restart is fine.
-Once your Mac starts back up again, sign back into iCloud through System Preferences -> iCloud -> Sign in
All should work after that!