For what it's worth, my fairly trashy* PC started to have a much easier time over the course of yesterday. When I first logged in (or rather, when I first eventually managed to get into the game) I had a pretty choppy experience through the tutorial, and despite dropping my graphics down to low I was having a pretty rough time moving around inside stations too. Alongside that, I was having trouble getting into any of the customisation menus - trying to customise a suit was taking so long that it would eventually give up and time out, and I also couldn't manage to get into the ship customisations to rename a ship that I'd forgotten I'd bought pre-Odyssey.
However, about a couple of hours in, as the servers became a bit more stable, I was able to access those customisation menus, and I began to see a little bit of an FPS increase as well. Nothing amazing, just a bump of 15-20, but it was enough to take me from constantly in the red (~20) to consistently in the yellow (~40) while moving around inside stations, and I was able to dial my graphics up to mid (and bump the textures back up to high) and maintain that. I'm tempted to go back in and redo the tutorial, and see if combat is any better for me now.
I'm not going to pretend this obviously proves some sort of connection between server load and people's framerate issues (I'm sure it doesn't), but folks who were having a really rough time of it yesterday might want to pop in with their graphics on low/mid and see if that's made any difference for them. I guess when your FPS is low to begin with, the small amount of effect from server issues is much more noticable?
(* GTX 1050 Ti, i5-2400 @ 3.10GHz, 16 GB RAM)