Hello Michi
Maybe it's a matter of definition how quietly you listen to music. I tested the best ANC headsets for silence at the beginning of 2023 (without music) and that's why they went back again, because there are already better ones.
I can't remember anymore, but I think with the Momentum 4 the noise was the reason and I'm personally very sensitive.
However, I can give you one piece of advice. Of all the top products currently on the market, the only one I haven't tried is the Apple one (which is also supposed to be great). In the end, I kept the Sony WH-1000XM5, which is ultra quiet and couldn't be better. I consider music quality to be a matter of taste, and the Sennheiser is definitely a pleasure to listen to. The Bose NC 700 also has a great sound and does a better job of removing voices than the Sony, but again it has a lot of noise (similar to the Momentum 4). By the way, the Sony is also one of the best in terms of wearing comfort.
So for sleeping, I can only advise against the Sennheiser and recommend the Sony. Other brands than those mentioned do not currently have ANC that is convincing for falling asleep.
You can find something nice in the 300-500 CHF price segment, but unfortunately not below that.
Hope this helps :-)
Kind regards

Hi, I use headphones to listen to music during the day. The app does allow you to adjust ANC though, I don't know with what results for your use.
Thanks

Hello, since I only listen to music with the M4 when I'm on the road, I can't say anything about this. Sorry!