More specifically I'm asking if getting stronger is inherently linked with getting closer to the center, or could get progress in stats just as efficiently by exploring systems on the edge?
From what I heard about ships, the amount inventory slots is very dependent on the amount of inventory slots your current ship has. Meaning that it can only have 1 or 2, and in some rare instances, 3 more slots than your current ship has.
From what I've experienced you don't really get better/stronger upgrades as you get close, at least not yet. I mean, I've got a bunch of Theta upgrades (they go Sigma -> Tau -> Theta -> Omega) and I'm in my third system where I've explored each planet a bunch and played 13 hours.
The crashed ships definitely seem to have around the same amount of slots as your ship, I've found some with 1 fewer or the same, usually +1 space BUT the ships you buy from other aliens can have varied amounts (they could be fewer, or they could have more than 40 and cost millions) so a decent way to get started on improving your ship is to save for a decent size alien ship (I bought a 21 slot one for around 750,000) and then try looking for downed ships. I probably should have saved a bit more and bought a bigger ship but like, a 28 slot one I saw was around 3 million and I kind of love my little Orange A-Wing (complete with what looks like an astromech droid!) that I bought off a Gek.
My first multi-tool was a good upgrade over the starter (had nice combat mods for the mining beam pre-installed and had more slots in general) but since then the tools I've been finding have been worse, but that could be luck.
So yeah, I think upgrades might just be based off random chance and what you have, though I've been getting a looooooad of dupes. There doesn't seem to be a surefire way to consistently make progress, like you can't save up and buy a blueprint for an upgrade, you can't add slots to your ship or go through an upgrade path there, you can't improve your multi-tool. The only consistent thing is upgrading exosuit slots which can be done at the drop pods with the glowy blue doorway things where each inv slot upgrade costs 10k more than the last one.