Handoff is not working

I don't have an explanation of why it has worked, and "is no longer working," but in addition to the steps you have already taken, review Use Handoff to continue a task on your other devices - Apple Support which states:

"Set up Handoff

Use Handoff with any Mac, iPhone, iPad, iPod touch, or Apple Watch that meets the Continuity system requirements. Handoff works when your devices are near each other and set up as follows:

• Each device is signed in to iCloud with the same Apple ID.
• To see the Apple ID used by Apple Watch, open the Apple Watch app on your iPhone, then go to General > Apple ID.
• Each device has Bluetooth turned on.
• Each device has Wi-Fi turned on.
• Each device has Handoff turned on."

What, if any recent changes. were made to your devices?

leisa204 wrote:

I'm running Catalina 10.15.4

I deleted pictures, PDF docs, and downloaded apps (parallels, zoom, ring central) that I don't use. I then emptied the waste bin and restarted the computer. I've never used any 'cleaner' applications.

Try starting your computer using Safe Mode: How to use safe mode on your Mac - Apple Support

"If the issue doesn't continue while in safe mode, leave safe mode by restarting your Mac normally. Then test for the issue again. The issue might be resolved."

leisa204 wrote:

Absolutely none. I’m now wondering if my capacity has maxed out, and I’d that has something to do with it. I’ve been furiously deleting documents and files.

I presume you are referring to your computer. What macOS are you using?

Why have you been wondering about capacity, and "deleting documents and files?"

What documents and files have you deleted?

Go to your Macintosh HD, select it, and use the keyboard shortcut (command+I). What numbers are listed under General>Capacity:/Available:?

leisa204 wrote:

I wonder if my mac needs 'defragmenting'...

The "Available" space is within acceptable performance/safety standards.

Your "mac" will not require 'defragmenting' Read: How to defrag a Mac (and why you don't need to)

What macOS are you using?

What documents and files have you deleted?

Are you using any special "Cleaner" Applications?

leisa204 wrote:

Oddly enough, I now see the my contacts and FaceTime won’t even open on my MacBook

What, if any recent changes. were made to your devices?

Great news!