I have the same issue and yeah, for me too, this was a primary purpose for finally purchasing an Apple watch. I have spent countless hours on the phone with Apple and talked with just about the highest levels of tech support as you can get short of an engineer. I have two sets of Jaybirds between me and my wife and a third set of some Chinese lesser brand. When I got the watch everything worked as it was supposed to. After a recent update that's no longer the case. All three pairs stopped working on the same day. One would think based of those facts alone that Apple would acknowledge the problem was with the watch or its software. Not so. I tried to have them exchange it for another watch but they found nothing wrong with it, which is probably the case since the problem is likely that they broke support for all of these third party headphones. We were able to test the watch on a pair of Beats X headphones, made by Apple and that seems to work, but they doesn't really do me any good with my or my wife's Jaybirds, which are generally superior headphones.
When I initially started researching the issue I couldn't find anyone having the same issue as me, so this board is reassuring. If there are other people having the same problem all of a sudden, then it is likely a software issue. Problem is, the jaybirds (X2 and X3) can't be updated, at least by the end-user. Given that Apple is in the earbuds business as well it's pretty suspicious when competing brands suddenly break. Ill will may or may not be the cause, but they haven't offered me any usable solutions to date in either case.