This has a strong Mass Effect 3 vibe to it - an ancient, supposedly invincible enemy comes to your door, takes over something large and important, and you have to collect assets and make sure they don't perish so you can actually take the battle to the enemy and defeat it. (Yea ME3 ending sucked af)
I don't know if you've watched Isaac Arthur's videos, but I believe these could get you some high-grade sci-fi ideas, at least when it comes to currently know science. I say it because "surviving universe's heat death" while blowing up stars and doing other stuff Shivans do is kinda... counterproductive. I guess I'd have a... more interesting idea. For example:
This would utilise the idea that, with expansion of the universe speeding up, at some point the spacetime would just... snap and rip apart (also based on an idea in one of Stanisław Lem's novels - that the universe is just a temporary exception from everything being just the ultimate void and could disappear at any moment). So there would be this kind of a space mind of some sort - composed of subspace or space itself, with Shivans being its physical emanation, with it being as aware of them as you are of your single body cells, the same goes for any self-evolved races (thus - the whole genocide thing). Due to universe coming closer and closer to the Big Rip, the Mind is either preparing, trying to bail out, panicking or being in a state close to agony (example: man swimming in a stormy sea, desperately trying to keep his head above the water). It would either try to preserve some of the spacetime together with matter in the subspace to eventually come back or stop the Rip altogether, doesn't matter. What matters is that it would require using the whole (for example) Laniakea Supercluster in some subspace magic way.
The notion here would be that, for example, the GTVA couldn't really damage the Shivans, but they could send multiple large fleets roaming through Shivan space, fending off attackers, and looking for answers (there are clues that it should work). They would be ignored by the gigantic stuff anyway. The general idea is that the main character, being in one of the fleets, gets exposed to *something* a couple times (maybe something like Bei and Laporte and others in BP), maybe also with others. Plot twist: the Mind has been through multiple cycles of barely holding the universe together only to do it again, again, again... (Big Crunch -> Big Bang cycles) and it effectively became an endless torment. At some point the fleet would start finding answers (maybe something alike Destiny from Stargate Universe, but in multiple fleets in multiple directions?), maybe some other parallel characters would be introduced, from other fleets or something, maybe there would be multiple parallel plot lines for multiple fleets, maybe with dead remains of some race with telepsychic abilities temporarily slamming the player into the realm of their own history (for a minicampaign loop) and imprint something onto the character himself, letting him experience something more than a normal man would. Some "mind connections" with others from other fleets or something like the Fedayeen Dreamscape could be included as a result. It would become a personal thing for the main character because nobody would believe him (thought as hallucinations and psychical stress, a result of lots of space battles - being in high-energy environment of a space battle especially with subspace distorsions taking place could be able to damage the brain without obvious external changes) so he has to deal with it and look for answers on his own - a personal matter. In the end, there would be a lot of space distorsions which would cause all the fleets to meet at some point, and some psychic cluster**** would happen and the player would discover yet another plot twist - that the Mind is actually human, but just upscaled to the whole universe and mad (Transcendant anyone?) with Shivans wiping out life being just a resemblance to human immune system. And in a pompastic, psychic ending, the player could make some decisions or something, with the available choices being based on his/her decisions throughout the plot. There could be also multiple characters involved though. It would be interesting to have the directions of multiple characters/campaigns converge and base the endings on player's actions in each one.
Man, I wrote too much. It even seems like a cool idea that might be made by someone at some point :P.