I finally got around to getting things set up, and for some reason, the container I created for jellyfin refused to allow NFS mounting.
I ended up trying a "Turnkey Media Server" template which ended up working. It also didn't allow NFS mounts, but it did allow CIFS mounting, which I used. Jellyfin is now refreshing the library. So far so good.
I tried to mount the share as NFS, but it didn't seem to work from the console in the container. I ended up using CIFS which worked.