The Immortality mod basically just makes players immortal, when you should die you are left with half a heart regardless of the cause of death, it works for all players present in the world.
You can choose which players are immortal with the command "immortal" use it to make a player immortal, use it again to make the player mortal again (There's a gamerule that is activated by default called immortalPlayers that makes all players immortal, to choose which players are and which aren't disable it and THEN use the command immortal)
The gamerule is called immortal_players since 1.21.11
In the latest releases you can use /isimmortal [player_name] to check if a player is immortal and /getimmortals to check the state (mortal/immortal) of each player
