If a player in spectator mode on a dedicated server starts to spectate a player, only the chunks around where they were when they started spectating them will remain visually loaded, and no new chunks will be visually loaded.

This means that if you are spectating a player who is constantly moving through the world, you need to de-spectate and re-spectate them to see the environment around them once they move into further chunks.

This is not the case for spectating any non-player entity.