@Russell_Dunn what are you running Zwift on, PC, Mac, ATV, iOS, Android?
Which Garmin HRM strap are you using? Is it a Dual mode strap (Bluetooth and ANT+) or just ANT+? Given your Edge is an 800, I’m guessing it is a little old and thus the HRM is fairly old also, thus an ANT+ strap only. Is this correct?
I have an older Garmin ANT+ and a 3rd party (CooSpo) Dual mode and Zwift on a Win10 PC seems to connect fine with both of them. I tend to use the old ANT+ one on the trainer so I can just leave it in the pain cave with the newer Dual mode with my road bike. So yours should work, at least if on a PC you have a similar setup to me. I don’t even have my Garmin Edge in the pain cave as I don’t want to deal with the complexities of devices connecting to it then switching to the computer.
Are you wetting the HRM strap contact areas to your chest before putting it on? If not, ensure you get the HRM strap contacts good and wet before putting it on your chest to ensure it begins transmitting.
If you have your ANT+ dongle on a USB extension cable, hold the dongle close to your chest when you put the strap on to see if it picks up. This is checking to see if it is a signal weakness problem. If not on an extension, get your chest close to the dongle to see if that helps it connect initially. Not that this is a good long term workaround, but at least it helps diagnose if signal strength is part of the issue.