I use Health Sync app
it syncs sleep and other data from my fitbit Air, except for (in my case) Readiness Score, Sleep score and Avg Sleeping HR. I manually input those data.
Sleep time, RHR, HRV, SPO2, Breathing rate are synced automatically (+ weight and fat% from my withings scale)
I have sent a request for adding the missing data from the automatic sync but so far nothing new from them