I’m not sure what’s wrong (it should work) but an ANT+ dongle can be quite inexpensive and still work fine. I can vouch for the Coospo RC401 which is US$11 on Amazon, and it’s nice to have a couple options for pairing. Sometimes a Zwift update will introduce bugs for one or the other and having options will keep you riding.
If you don’t get useful suggestions here about the Bluetooth problem, contact Zwift support and they may be able to figure out what’s up.
If you do buy an ANT+ dongle, review this thread: