What filesystem are you using on the external drive? If it is NTFS or FAT, they won’t store permissions on the filesystem, which would explain why the owner/group changes are not persistent. To fix that, you can set the uid/gid on mount in your fstab.

/dev/mapper/YOUR_DRIVE /path/to/mnt <fstype> rw,uid=<jellyfin_uid>,gid=<jellyfin_gid>,dmask=0002,fmask=0113

Are you using the default bridge? I have a similar setup (with Traefik instead of NPM), and for each compose file am using separate networks for the internet, proxy, and backend services.

services:
  some_service:
    ...
    networks:
      - frontend_network
      - proxy_network
      - backend_network
  backend_service:
    ...
    networks:
      - backend_network
networks:
  frontend_network:
    driver: "bridge"
  proxy_network:
    driver: "bridge"
    internal: true
  backend_network:
    driver: "bridge"
    internal: true