The one thing I'll say on the subject of the story (since this is supposed to be a topic about the game play) is that V's overall story influence feels like an overt side effect of the game's writers treating Vergil himself - and its overall narrative - as fanservice. Dante and Vergil choosing to fight each other, along with the plot being hijacked the moment Vergil is resurrected, all exists because "why else should Vergil exist in DMC if for no other reason than to cross swords with Dante?" In the end he has the effect of being a black hole on the narrative, almost entirely existing as a means to relitigate the iconic sibling battle.
I genuinely consider it sort of a consequence of the game's long hiatus period that characters like uncle Dante and Vergil became deified in their iconography that DMC5 subtly exists as a "greatest hits" retelling more than anything that concretely is meant to serve as the conclusion of Dante and Vergil's sibling rivalry, because even in the context of DMC itself, much of the things that's still held up as classic about DMC3 are things that only really encompass a fraction of the series' overall content. Nero himself is hilariously de-emphasized throughout the campaign despite the fact that the torch should be passed on by now, though it doesn't ever quite feel like that's the case.
And who knows, maybe that was enough this time given the series' absence, even if the narrative ages in such a sour way under scrutiny that you sort of realize DMC5's plot feels like they mixed the beat-for-beat elements of Street Fighter V and MvCI, just with more charming character writing.