A follow-up on this for whomever may be having the same issue - the problem was coming from the fact that my internal network was set up with an “abnormal” IP range that wasn’t following the 192.168.*.* pattern. Even though the Shield was getting connected to the internet and various services were running normally the allocated internal IP was messing up the Samba server and it was seeing the internal IP as external making it think it simply just doesn’t have an internal IP at all. That killed the Transfer files over local network functionality with an error message “No ethernet or wifi connection” and it also seemed to affect the PMS itself and made it unreachable/not-claimable through the web app.
Once I changed my router settings so my internal network follows the RFC 1918 standard, factory reset the Shield and re-updated OS and apps the sharing feature started working and the PMS appeared normally.
All this was made possible by the great guys from Nvidia’s support team which spent almost a week debugging with me.