I've previously argued that SW and 40K are perfectly compatible and you can quite realistically investigate this kind of cross-over and its effects... if you treat the Force and the Warp as fundamentally the same thing, but with a different condition in the two settings. In SW, you get the Force: essentially the Immaterium manifested as an "energy field generated by all living beings", which is generally harmonious, and only to a degree afflicted by the influence of the darker impulses of sapient beings. In 40K, you get the Warp: which is the same Immaterium, but heated and stirred (as it were) into a frothing cauldron of frenzied passions.
My hypothesis is that the cataclysmic events and unmatched horrors of the War in Heaven caused the Immaterium to become so, ah... warped. I also view Hyperspace (inherently a plane of existence where mass and matter can be discounted, thus allowing FTL travel) as fundamentally skirting the ede of the Immaterium. In the setting of 40K, this thin membrane appears to have been dissolved into the Immaterium.
Applying that thesis to this scenario, we might venture a guess as to the implications. These end up tracking quite well with the premises of the OP.
First off the "gods" manifested in and by the Warp are created out of the passions and guiding notions and impulses of sapient beings. The War in Heaven brought forth (or at any rate: brought to greatness) the Ruinous Powers, their great strength (combined with the collapse of many barriers between Materium and Immaterium) allowed them considerable direct influence in the Materium, this in turn allowed them to sway many to serve them and worship them, which in turn increased their power again. A self-perpetuating mechanism.
In the SW setting, the barriers between Materium and Immaterium remain; and Hyperspace remains "on the surface" of the Immaterium, rather than having collapsed right into it. Furthermore, the collective psyche of the galaxy's inhabitants has never been so utterly ruined as was accomplished by the War in Heaven. Even the domination of, and uprising against, the Rakata appears to have been far less of a "Big Thing". Indeed, it even has positive, optimistic connotations in the vague cultural memories of those who triumphantly threw off the yoke.
All of this explains that, if transplanted to the SW setting, the Ruinous Powers will be unable to directly influence much of anything. They are far more cut off from the physical universe, and the "background psyche" of the galaxy is in much less turmoil; so there's less for them to easily exploit.
On the other hand, a whole shitload of their followers has just been dumped into this galaxy, and those retain their worship and dedication-- which explains why the Ruinous Powers do promptly manifest in the setting. Although in truth, they'll be much-reduced, less-powerful instantiations of the same ideas (in the Platonist sense).
The further implication (not stated by the OP, but derived from mu train of thought here) would then be that the forces of Chaos lose much of whatever "supernatural" power they derive from the Ruinous Powers. There's less power to give. Indeed, the power that is there... is the Force. Which is this setting's manifestation of the same "energy generated by all life".
The Force is less inclined towards "personalised" manifestation (i.e. "deities"). Insofar as the galaxy's inhabitants have collectively manifested these, we must point to the Ones, of Mortis. A triad of a father (who maintains order), a daughter (who creates new life) and a son (who destroys). This is very much akin to the central Hindu triad of creator-preserver-destroyer. Representative of the natural cycle of renewal, as it were.
(An instantation that comes closest to the typcal 40K approach -- although still far removed from it -- may be identified in the Goddess cult of the Pius Dea movement.)
A very striking result is that whatever "dark" impulse is manifested in the Force does not take the shape of a distinct "god", but rather appears as a more selfish realisation. Dark Siders are not like Chaos adepts, because they are too egocentric for that. They become atomised away from all others, whereas those who are in the Light are all linked together in supernatural harmony. This may be the natural state of the Immaterium, or it may just be a result of the dominant "trends" in the thinking (and feeling) of sapients in this galaxy.
At any rate, it suggests that if the imported Chaos legions seek more power, they'll find it by becoming... more like Sith. By adapting to their new situation, and seeking out the sources of power that it offers them. And in doing so, they'll be afflicted by the same weaknesses that beset the Sith (and all Dark Siders), in that they become more atomised. More self-centred and self-obsessed.
Possibly to the point that subjugation to, let's face it, those now rather distant Ruinous Powers becomes less and less attractive. Thus leeching away the power of Chaos, and slowly turning the legions of Chaos into something far more like a Sith Empire.
(And, conversely, if a Sith Empire of old were to ve transplanted to the 40K setting, its Dark Siders would just as surely become swayed, and ultimately dominated, by the Chaos Gods.)
I think one of the limited things in 40K (especially in comparison to say Warhammer Fantasy) is that when you die in 40K, in most cases your soul gets nommed in the Warp so basically a crapsack ending almost regardless. There's exceptions, Aledari Crystals for the Exodites, devoured by C'tan shards, consumed by the Hive Mind and other grimdark nonsense but by and large, unlike in Warhammer Fantasy where souls and the afterlife is basically "undefined" the Chaos Gods apparently get nomming rights on all souls. That wouldn't be the case here so to speak. They would have to nom their worshippers souls... or harvest things from sacrifices and the like as per tradition.
The point of this initial ramble being that there's more divine diversity potential in the
Star Wars verse and can help with making the plentiful divine biodiversity that I'm really looking for.
There is definitely a lack of personalization in regards to Deities and the Force is a thing which is far more stable supernatural force then the Warp as you state as well which will impact the influence of the Ruinous Powers as well. There's a lot of religion in
Star Wars but it always takes the back burner in most cases.
The fact that the Sith are Egocentric is an important observation that you made as well. As another illustrative example, it's like the difference I feel between seeing Viltrumites versus Saiyans in a 40K Warp Style setting IMHO. The former are so self centered and smug and egocentric, they would be more resistant to Chaos corruption, the latter however seem like they could fall to someone like Khorne far more readily. There could still be Chaos influenced Sith of course but it wouldn't be something to be taken for granted in a Universe with a far reduced presence in the Warp.
Putting the Ruinous Powers and Chaos in the Unknown Regions would help give a reason for why the Unknown Regions are the way they are because... I've read the Disney (via
Fallen Order) and KOTOR explanations for why the Unknown Regions are the way they are and the former seems kinda balls and 40K-lite (and Dune lite as well with Force-sensitive Navigators lol) and the latter is better but does seem kinda War in Heaven-y. But then again, a Great War (Infinite Empire era perhaps) is how the Ruinous Powers came into being in 40K so why not something similar in Star Wars. The other alternative is they just arrive because of the sudden influx of their worshippers arriving.
Either way, the Ruinous Powers arriving and having a power base in the Unknown Regions can help reason why the Unknown Regions are that way. Maybe Ruinous powered sorcery is more powerful there, but the Force is still just as strong there as elsewhere.
Anywho I would prefer the Ruinous Powers and Chaos Worshippers kind of being their own thing instead of becoming more Sith. I'd like to think of them as generally distinct entities, though I like the idea of Chaos worshippers being more Sith in the case of those worshipping and adhering to the Dark Side of the Force and preferably some sort of eldritch/divine Dark Side entities, like mentioned before with what Palpatine wanted to be... or an entity like Darth Nihilus from the KOTOR era. While Palpatine is kinda Tzeentchy... the idea of him being a concept of Dark Side 'Order' would make him distinct from
Chaos Gods rather obviously. And Nihilus would have his own thing going on as well that's distinct from the four Ruinous Powers as well.
And like you (and others) referenced, the idea of the 'The Goddess' from the Pius Dea era could be another Force type God and very, very Humanocentric of course.
For the default 'Light' Force I'd still like to see the general following of The Force being more widespread then just a monastic order of Jedi. Like a semi-official religion of the Republic and other goodly normies of the Galaxy. But like I said in my original post, I'd like to see more diversity in the Jedi Order and general Force adherents. Instead of divinity, it can be more philosophy and ideologically/theologically based. They're all adherents to the Living Force as a concept, but got different ways of perceiving and viewing it. So not a personification of Force deities like you'd see with the 'Dark/Sith Gods' since that's a corruption or with 'The Goddess' deity either.
The entry of the Warp entities into the Star Wars Galaxy making personal deification possible is a neat concept I'd like to see explored including divine entities 'conceived by The Force' since the Prequels made that a thing... for some reason.
Didn't really comment much on the trinity with the Father, Son and Daughter and it's relation to Hindu traditions because.. I never really was interesting in that particular plotline in
The Clone Wars.
/ramble over