https://developer.chrome.com/blog/private-network-access-pre... is one idea being actively worked on in this area
The "new material" is https://developer.chrome.com/blog/private-network-access-upd... and changed from restricting all "public websites" to only restricting non-HTTPS sites.
It does at least say:
>Restricting private network requests to secure contexts is only the first step in launching Private Network Access.
... so maybe it'll become better later.