I have to say, the Bluesky bridge is confusing for me(!)
I don't use it myself but sometimes I respond to posts and only realise much later it was from a bridge account, in which case the user may or my not see my reply. I certainly don't see my reply on Bluesky. Same thing can happen vice versa.
I don't want a compulsory opt-in to another service, I want the AT and ActivityPub protocols to be compatible. In lieu of that the bridge accounts need to be a lot more obvious in their presentation.
Right now I'm not sure if the brid.gy service makes things better or worse but it feels like the latter to me.