Hi @ahearingaid,
You’re describing the Holy Grail of headphones and they may be tough to find!
The problem as I see it is that headphones amplify all sounds equally, whereas hearing aids only amplify the sounds you need to understand speech. By amplifying everything, headphones just make speech that is difficult to understand louder. Making the source louder can help a little, but nowhere near as much as a hearing aid.
Instead of purchasing a headset, are you able to purchase a device that will stream sounds directly to your hearing aids? I can do this, and I find it makes a big difference for things like listening to music, audiobooks, TV, and especially video conference calls.
Hope you find a solution!