Installing the Jellyfin add on into kodi takes a few minutes. Nothing much to consider, just try it and see if that changes anything.
I have a similar setup (rpi with OSMC, media hosted on file server) and prefer using Jellyfin as the source for all clients, as it keeps track of watched status across everything. It's not perfect, but better than without Jellyfin.
Tangent, unsolicited:
Music lessons over video call, that has to be a real pain. I can't find it now, but there's an Adam Neely video where he talks about why online recording sessions can't work, as transmission latency works against the immediacy needed to play music together. He said it better than I can.
Except if your idea is to play in turns, but then capturing the thing you want to show... Can't you find another teacher closer to you?