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I do actively play, yes. Story? Some. When it first came out there was only a very thin, ambiguous quest line designed to get you to travel to the galaxy centre and to another galaxy (there being 255 of those). Since then they've added several tutorial quests - almost every time they add a significant feature, like pirate systems, there's a small quest line that introduces you to the concept - and a less vague (and quite subtle, clever and occasionally funny) quest line that has some deep philosophical things to say about the nature of the No Man's Sky universe and provides another route to travelling to another galaxy, but they're hardly rich stories and once you are in your second galaxy you're back to roaming and base building.
There's an unusually wide range of things to do (base building, exploration, managing a trading fleet, fighting pirates or being a pirate, derelict space freighters with rogue security systems and dangerous creatures, undersea exploration, all kinds of land vehicles and even a mech) but none of those things is as deep as they are in games that specialise in one of those things. It stands somewhere between Minecraft and Elite Dangerous. And one of the things it shares with ED is that you have to create your own purpose and story. Another is that playing it is a bit like having a job.
To be honest, I'm still playing it because when they added VR they did it better than many games which were designed for VR from the start. Almost every aspect of the game is more fun in VR, particularly the vehicles and the space combat. Otherwise I'd have moved on after a while, or just be dipping into it once or twice a month.
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If by "now" you mean with this update, they haven't changed the story but collated all the lore you discover, in one place for you to refer back to. [shrug]
I don't think it's particularly story-driven and you'd likely be disappointed if you want something with a strong narrative.
My "sweaty" (+2k hours) take, is that NMS is all about the journey, not the destination: ie it's not about actually getting an S-class this or min/maxing that, it's what you go through to get your S-class this and what you learn min/maxing.
No Man's Sky update dropped yesterday. Bit of a rebalance, although nothing on a Blizzard scale; minmaxers and glitch exploiters had some of their toys taken away. Major meltdown among the more childish segment of the player community, death threats to Hello Games staff on Twitter and elsewhere. Also mobs of angry PC users attacking Switch users in general as if they were to blame (a Switch port also dropped yesterday), despite the changes being completely orthogonal to it and the Switch version not even having this update yet. Sheesh.