I have Oticon OPN S 1 hearing aids and a ConnectClip.
I requested a bluetooth compatible VOIP phone at work (a University where our building is VOIP only with Cisco equipment). I was provided a Cisco 8851 which has an improved audio system compared to the original (and quite old) Cisco VOIP phone I had so it is better as a (normal) phone. It pairs with my ConnectClip - the ConnectClip and hearing aid combination become a Bluetooth “headset” for the phone. The phone controls work for changing volume and muting the microphone in the ConnectClip. The combination works OK for me in most circumstances but the ConnectClip microphone is quite sensitive and it picks up room noise (especially the AC fan in my noisy office). So it is not a good combination for conference calls unless I keep the microphone muted except for when I speak.
The Cisco 8851 can also pair with the iPhone - I have not tried that feature. I have not checked recently to see if Cisco offers newer and/or improved Bluetooth capable phones. One feature the 8851 offers is a Wideband audio codec that is supposed to improve voice quality as compared to the normal codec typically used. The University has chosen not to offer that codec to users although Cisco recommends it for use with conference calls and other uses where improved voice quality would be useful. If you ask for a new phone, you might also ask that they offer the improved voice quality codec with your new phone - I think it is the G.722 codec. Your phone/network people should know.