I think it won't be quite as existential, despite how well they make it all feel rooted in reality, it's still pretty easy to keep in mind that it is a videogame. And with default settings and leaving "flight assist" on, the space ships handle more like planes. You can always disable flight assist, or have it on a toggle, or "disable when button held" setup too. Or, enable when held, if you want to be free flying most of the time, but still have a "stop" button when you want to cancel out your inertia, or more accurately match it with your current frame of reference.

Basically, by default, you don't have to think about your frame of reference. The fact that it is a videogame basically takes care of that. It's a convenient way to hide that the instance you are in is faking(incredibly accurately) everything else that is not in your current frame of reference. Despite space travel feeling pretty seamless, it's just cuz they hide the load screens and instance transfers as just part of navigating space. Any time you are unable to touch the controls, that is a load screen. Even if it otherwise looks the same, most notably when entering or exiting a planets frame of reference and switching between the "space" graphics of the planet to the "terrain" graphics. When approaching a planets gravity well, you basically do an uncontrolled glide that transitions you from space appropriate speeds to surface appropriate speed. That speed transition is the loading screen.

Probably the only thing that might give a similar sense of existential dread for a few seconds is if you jump to a binary star system at a time when the star you aren't jumping to just happens to be in the same direction you just jumped in from. It will look as though you flew through that star. The odds are pretty low, even full time explorers rarely see it, but it is something that can happen.