Core connected to BT Home Hub 5: I cannot get any error message because Roon on PC cannot then see the core. However, Roon ARC on mobile device still cannot make a connection to the core (“nor accessible outside of your network”). My ISP is BT, one of the biggest in the UK and does not offer static IP addresses. I don’t understand why your implementation will not work on my set-up when I have access to my Synology RAID from anywhere in the world via DS file app on mobile - naively, it seems to me to be the same sort of requirement.
You don’t need a static IP; a dynamically assigned IP address works.
Most likely you have multiple NAT since you are using Google Nest with the BT Home Hub. This is clear in the status message you posted.
Please look at this guide, especially the section, Multiple NAT.
NAT lets all the devices on your network share a single “external” address, via your router.
However if there’s more than one device between your Roon core and the public internet which are both configured to do this “translation” process, Roon won’t be able to configure your network to allow access to your Roon Core.
No need to buy a modem (I’ve not used BT for some time, and thought they offered bridge mode), but instead set up port forwarding to Google mesh in the Home Hub. Then repeat this with Google mesh or use UPnP.
Make sure that you use the same port as shown in Roon ARC settings for both.