"A story driven by main and side quests."
To me this is already there. The story is that the world as we knew it is gone and now taken over by zombies and other abominations. The main quest is to survive in the middle of hell. Side quests are doing things that help, like establishing contact with traders, building bridges to cross rivers easily, exploring towns and cities for extra things that aren't crucial to helping you survive, but making it easier or bolstering your base.
I'm a long time gamer of survival horror and crafting games. And when diving into another, these things are just done with no thought. But after a while, it became just another game. A friend of mine who is huge on role playing showed me how to do what comes as second nature or as parts of playing the game as ways to set goals or make quests out of them. Give yourself quests.
Quest 1.) Gather 1,000 lumber/iron.
Quest 2.) Craft X amount of Y.
Quest 3.) Find other life. (Traders.)
Try not to burn through content and pace yourself as if it were actually you in the game and go from there. It also helps if you can make friends who are willing to add role play elements to the game as well. Make up tasks, such as use the gyrocopter (when it's out) to do some air recon and look for a good place to start another base. Get in there and use your imagination to the fullest. Get crazy, silly, serious. The only limit to the game is yourself.
For me, a story in a well made survival game only adds some flavor and is uneeded, mostly because of the reasons you mentioned. As long as a game is engaging enough and presents challenges you must overcome to survive, you make up your own "quests" and complete them in the order you like in order to survive another day.
But I think that if there is no real purpose or practical need for these "quests" (e.g. a point when you no longer need wood to craft anything, but you still gather wood as a personal quest), you might as well be playing one of those clicker games on steam. Moreover, RP is great and can enrich a video game, but imo, if a video game *needs* RP in order for it to be engaging, then you might as well be playing PnP, DnD, a MUD or RP in some VR chat, if you also want a virtual world around you.
One other thing I do not agree with, is "having to pace yourself as if it was actually you in the game and not burn through content". First of all, if it was me in the game I would certainly burn through content as fast as I can

But in general, I don't think it is a good thing to have to forcefully slow things down, so that the game won't become boring. It should be up to the game and its ruleset - not to superficially block you from further progress - but to throw enough things at you so that it keeps you busy. And that brings me to my next grievance mostly irrelevant with the topic or what you said.
And this is surely an unpopular opinion but I have to get it out of me - while 7D has the makings of a *great* survival game, it just stops being enjoyable after the relatively short "wood/stone to steel curve". So, my experience ends up like that - I scavenge in towns for things I don't really need (scarce loot abundance), stop hunting because my food supply is ridiculously large, build a garden but then get disappointed because I never needed one in the first place, getting infected searching for anti-biotics and then not bothering using them, hide instectively in a bunker at night only to safely stare at the wall, eventually stop caring if I die (even with loot deletion) - I could go on all day. I don't think it's content that is missing, it's mostly cohesion of existing content. Then again it might be an early middle age crisis, I don't know anymore.