Hi Guys,
This issue was quickly resolved for me after I called Apple Care. Follow the instructions below.
After the Monterey update
Make sure all devices are on wifi
make sure bluetooth is switched on all devices
(the most important) on your iPhone/iPad settings/general/airplay&handoff/swtich on "handoff"
(the most important) on your MacBookPro Settings/General/then at the very bottom of this screen check, "allow Handoff between this Mac and your iCloud devices."
If Universal Clipboard is not working and you 'have not' updated to Montery
make sure that all devices are running on the same up-to-date versions/updates