Escape From Tarkov is a semi open world FPS PvP and PvE realistic survival shooter, with emphasis on looting and an in depth weapon and inventory customization. There are plans for full open world in the future. I believe it is in alpha right now, not sure if it is technically early access or just a closed alpha.
The inventory system is very similar to DayZ. You lose all your gear upon death so the key to playing is to loot as much good gear and escape the map with it to be able to keep it. It is then stored in your main menu storage which you can then use to take back into levels with. There is also a trading system and there are lots of bulk/junk items you can find to sell in each map. You get a small storage slot on you for items you don't want to lose on death which makes it handy if you are looking out for a particular thing, but it is too small to be able to store primary weapons in. There is a requirement for eating and drinking however I am unsure how much that is focused on right now as it is in it's early stages of development. There are also indicators for radiation and bio levels so much more features seem like they will be added later. It has an insanely detailed weapon customization mechanic that pretty much trumps any other game in existence.