Emanuele_Barone Glad you found a solution to your space problem. And there IS a way to make OneDrive work with the home directory on an external drive. I'm not sure what the exact cause of the problem was, but I do know that if the home directory is offloaded to external storage with the "Ignore ownership on this volume" option NOT set on the external volume, OneDrive works fine that way.
There are two possible reasons for the earlier problem, and I haven't yet bothered to sort them out:
1. The space in my home directory on the external drive was owned by UID:GID 99:99 (unknown:unknown). Likely the directory housing the sync root was as well, and this may have prevented OneDrive from working properly.
2. Or, it could have been a direct consequence of the reason why my home directory wasn't owned by me: when I first formatted the volume, I didn't know there was an option to ignore ownership on the volume, and it is apparently the default when formatting an external drive - this can be set in the Get Info dialog if your account has admin privilege and it can probably also be set from Disk Utility, but I didn't know about this at the time. Man diskutil (8) explains that when disableOwnership is set for a volume, everything on it appears to be owned by the current user, and that's exactly the behavior I observed. It's possible that having that option set prevents AFP from syncing from the cloud to the volume.
Anyway, I have OD working now the way I want, so I'll stop ranting here unless something else appears to be broken. 😉