Wow, just wow.
You think Rust is a shining example of a sandbox game. Poor you.
PvP is not the pinnacle of sandbox games. Otherwise World of Warships/ Tanks / Planes or War Thunder would be your ideal game.
The most noteworthy sandbox game is Minecraft, they give you the tools to work within their world and a few NPCs to interact with - apart from that, you're on your own.
Same goes for Ark: Survival Evolved. You get an environment, the tools to master it - and the rest is up to you.
Both games have PvP / PvE options. Both games are sandbox games. Both games require the player to have an imagination to make the most of it.
Sounds and awful lot like Elite: Dangerous to me.
Oh, by the way -
Rust has PvE. So yet again you're not being honest.
Any game with NPCs, has a PvE element to it. As NPCs are part of the "environment" (Hint: the "E" in "PvE" stands for "environment")