An important aspect of it is whether the nation is "at war" for the purposes of signing defense treaties (or being forcefully vassalized). Fluff-wise the war might still be on, it's just that the chaos of the situation has given way to a temporary detente. New de-facto borders are drawn, and both states are recognized as sovereign enough to sign agreements without explicit duress.
Because wanting to swoop in and interfere with a war is something you're supposed to declare beforehand by "guaranteeing independence", which costs influence because you're establishing an international policy. You *can* still screw with an existing conflict with your own casus belli, which I have done to save minor states, but you don't get treated as a savior or gain a vassal for it because you didn't go through the proper channels. You didn't make a promise or a warning, so it just looks opportunistic (and likely is).
But during a period of truce (white peace) you can totally offer protection (or "protection" $_$) against the next wave, and be taken seriously.
I'd love if war was a bit more dynamic than the stilted "declaration of war/established peace" done now. I've been imagining a system where
1) closed borders doesn't actually prevent other empires from entering your borders, it just allows you to intercept/shoot them down if they do with very little repercussions (and you could do some Galactic Community laws on it as well),
2) Empires can always attack each others ships/fleets and invade planets (assuming their policies allow it),
2.1) once you have military control of a planet assuming full control of it is a lengthy process that requires expenditure of influence, military presence and possibly has events associated with it; and
3) when an empire fires on another empire the attacked empire can react with formal denouncement and/or declaration or war, or try and initiate more peaceful proceedings to prevent a war.
Having claims on systems would give reduced influence cost for integrating a conquer system since you've done some of the work pre-emptively, at the cost of diplomatic relations, and would also lead to less threat as you've stated your claim to the galactic community officially beforehand, instead of just suddenly "invading Poland".
I feel like the Galactic Community should also have an overall "ethical stance", affected by the diplomatic weight and ethics composition of its members. If the majority of the diplomatic weight of the GC is militants or authoritarians for example, there'd be less diplomatic impact for conquering and subjugating while the diplomatic impact of that would be great if the GC was pacifist and egalitarian.
The current "formal" war declarations could still be kept in the game and be used to lessen the diplomatic impact of your aggressive actions as well, hopefully creating a more dynamic Galactic Community. Empires would also be able to affect this "ethical stance" through the use of Envoys and favours.
For added granularity, you'd also be able to set your diplomatic stance towards other empires individually so you could maintain amiable relations with some empires while embargoing/isolating/bullying others, which of course would lead to various diplomatic modifiers. I like the current ability to set your diplomatic policy but it really needs to be possible to customize it individually