There are resolutions to all the quests, yes, but you'll come across the pieces as you explore the universe. You are pretty much on your own now, but I can offer a few tips to progress I think.
You can ignore the base computer quests, and the settlers - those are endless for you now, I think. Something more interesting will pop up from them if it's a major story beat.
As far as what you're even looking for: Do you have all 16 glyphs? Have you saved any freighters in battle yet? Looted a derelict? Tamed a little companion buddy? Have you made it to the centre of the galaxy? Got an organic ship? Got a fleet? Can you travel to any colour star? It took me ages to find the Constructs, dunno if you've run across them yet... And this is far from a comprehensive list. It's a big universe with lots to find!