The FR935 only broadcasts HR in ANT+, it does not broadcast it in Bluetooth like the newer versions. If you’re using Zwift on a PC/Mac you can pair your watch directly to Zwift in game using an ANT+ dongle.
You can pair HR monitors directly to the Zwift Hub for bridging via Bluetooth but I don’t know if it does with ANT+ (I would guess it doesn’t but not sure).
Personally, if you really want your HR to be accurate, I would suggest buying an actual HRM, anyway. I have found that the HR coming from Garmin watches to be VERY suspect during activities. You can likely find a good one on Amazon, that will broadcast both BT and ANT+, at a reasonable price. I have a Coospo that, I think, cost around $30.