Will probably buy me tomorrow a Sony TV set, because they build for me also very good phones and I'm generally satisfied with the brand. Now it will be a model that also supports HDR on TV. My question would be synonymous, apart from this TV-HDR have other advantages in this "networking"?
No, you will not have noticeable advantages.
The TV or PS4 may recognize the connected device. But that's nothing that makes a big difference now.
A kind of networking, as with Apple, you will not experience here.
Of course, you will still benefit from the HDR feature anyway. If other devices support this as well.