This is not correct. It should work for the self-hosted too.
And that’s good because I can’t see Apple closing this gap. It’s an unacceptably dominant pseudo-monopoly. Were they to implement web notifications on iOS that would be yet another reason not to bother with creating a app specifically for their proprietary App Store to then have to suffer revenue sharing and/or the additional build and maintenance costs. Were law makers sophisticated enough they should probably have legislated for this already. Don’t let that stop you contacting your representative: not providing web notifications is highly anti-competitive!