I am facing the same issue on an iPhone 6s ever since updating to iOS 14 (now on 14.4). Every pair of bluetooth headphones I try, get disconnected if you separate 1 meter or if you move with respect to the phone. I found a temporary solution the an apple forum (I cannot find the link right now) which consisted on enabling the personal hotspot. That would temporarily fix the issue. But again, after some minutes, it is back to unstable. It's very annoying.