Probably not what you are looking for but Call of Duty Zombies is a timeloop. Every match you play is canon to the lore. Black Ops 3 on PC is probably the best one to get since it has the most of the maps from earlier games + Steam workshop support for custom maps. Most levels even have ways to beat them and break the timeloop which will provide a cutscene with lore drops.
If you and some friends can get the game on sale the base game alone is great without DLC just for the endless amount of content in the workshop.
I don’t play any mobile games so I unfortunately don’t know any recommendations but if sandboxing an app that doesn’t respect your privacy sounds like a good solution to you, you could try shelter. Additionally, the Aurora Store can show you what permissions and trackers an android app on the Play Store uses.
I actually have a Steam collection for this. It’s mostly games I play when I have a handful of friends over. My favorites in the collection are: