I was using this mod on version 1.21.4 and noticed that when I toggle name tags off, the lead connecting the player and a tied entity turns invisible. I don't know if this is fixable, I do not know whether the same issue applies to fishing line, but I thought it was an important bug to report. Good luck if you ever decide to look into this.

Good catch! This is fixed now in version 2.1.3. You can download this update on GitHub or on Modrinth.