I would like to play online with random people. Not necessarily with them but just being able to run across people while I am playing. But I don't see options for this. Would anyone be able to help guide me?

None of my friends have GOG nor even play NMS so looking for human interaction sometimes when I play would be nice.

This.

They should make npc Followers (hired guns or workers) to keep the Player company so he don`t feel lonely.

A little obvious but visit the space anomaly. Hit x while in space, one of the main story lines should get you there. Plenty of other players there as it pretty much exists just so people can meet up these days.

That'd be the Nexus, yes? But then the people are only visible in there. Can't really encounter them randomly anywhere else- and the title screen option doesn't seem to be working either.
That's a bit of a disappointment, sadly.

The best way to play with people who aren't friends is to do the missions in the Nexus. Otherwise you need some friends to play with and meet up somewhere. You're never going to randomly encounter anyone because the galaxy is so large that if everyone on Earth was playing most of the planets would still be empty.

Well, at first I just kept my game open for others to join.
It didn't happen very often but there were random people that would show up in the same system and I think it only happened once where I actually bumped into someone on a planet. It were still times that other players not in your group would show up as just floating lights.

So it is possible but very rare.

After I left Nexus I noticed a person roaming around my base, that was my first time in 10 hrs

Most initial spawn points for new games are in a narrow disk near the periphery of Euclid. While you are in that area, scan for nearby discoveries and warp over to those systems.

The odds are still very low but far better than a random encounter. Many players will build their initial base within a few hundred LY of where they started, so they're out there somewhere. Happy hunting!