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Absolutely. They are not going to share metadata or things like played status, but I have been using both simultaneously since almost the first day I spun up my media server.
I definitely prefer Jellyfin overall, but Plex is more convenient for sharing with less techy family so I keep it spun up. Jellyfin also requires some finicky network configuration (so I have heard) to cast media to a Chromecast, so Plex wins out there.
Not OP, but I can answer part of your questions:
I have Plex and Jellyfin running off the exact same media library no problem at all. So there should be zero need to modify anything–if anything Jellyfin seems a little better at catching “extras” folders than Plex.
The Jellyfin app plays music–but it’s definitely NOT a music app. I always hear Symfonium highly recommended, but have not yet given it a whirl myself.