Yes, Black Ops 3 is still active on Xbox One. Despite being released in 2024, the game continues to have an active player base on the Xbox One platform.
Worry not about PVP: There is a maximum of 24 players in each server, but Modern Warfare Zombies (MWZ) is a PVE-focused game mode within Call of Duty: Modern Warfare III. Work together or ignore other players entirely.