Your notion of wonder-starbase-superstructures is an intriguing idea. That being said, the notion of solar powered anything is fairly silly. I'm not sure if it's a translation issue, but you probably want something more akin to the Star Forge - https://starwars.fandom.com/wiki/Star_Forge

It's not sunlight powering said starbase\automated shipyard, rather it's using energy and matter drained from the star (in conjunction with Dark Side Force power?). Obviously the SoaSE universe doesn't have Force stuff, let alone Jeth or Sidi
but a 'wonder-starbase-superstructure' type victory might be plausible. Perhaps a base structure with extremely slow upgrades required to complete the victory thereby forcing a star rush? Or which gives such overwhelming advantage that the game snowballs thereafter - a superstructure equivalent to a titan?
(How would this work for multi-star maps though?)
While the Primacy killing other planets (Novalith doesn't crack planets does it? Oh my bad - https://strategywiki.org/wiki/Sins_of_a_Solar_Empire_II/TEC_Ship_items#Planet_Cracker_Warheads) makes sense, why is it a problem if the Enclave 'nuke' enemy worlds? Their strategy is turtle up then wipe out external life. An economic structure simply doesn't offer a victory option. Remember, Vasari don't even use credits!
Wrath killing or mind controlling their enemies makes sense, but Reborn getting a 'teleport anywhere' power does not. Vasari are the (current) phase masters. The Reborn's teleport to the homeworld seems to challenge this. Allowing them to increase this to teleport anywhere would be grossly overpowered. Something more akin to 'resurrect for free any friendly vessel killed within range' would be more reasonable IMHO, also more consistent with the nature of the faction. There'd need to be a resurrect delay e.g. 2 minutes for frigates, 4 minutes for cruisers, and 5 minutes + 1 minute per level for capital ships, but this would force enemies to do a hammer blow to knock it out, or lose. Likewise the Wrath could simply take over planets in an expanding arc, forcing enemy forces to charge the star with their combined fleets, or lose.
While I get your Exodus Core Stripper point, I don't think it's viable. The Jarrasul Evacuator has Drain Planet as its ultimate, which is somewhat akin to https://strategywiki.org/wiki/Sins_of_a_Solar_Empire_II/Stripped_to_the_Core, just far weaker, and non-destructive. I don't see a way for the Exodus to manage the same thing on an interplanetary, or interstellar, basis. Maybe instead resurrect SoaSE 1's Kostura Cannon?

https://sinsofasolarempire.fandom.com/wiki/Kostura_Cannon
In conjunction with Tier 5's Highly Attuned Sensors which allow for every phase jump to be seen, and to know exactly what's jumped into every system, the Exodus would be able to hit fleets the moment they jump into another system, and absolutely wipe them out - unless it was a wormhole system, but even they'd be limited to the other side, the moment they phase jumped away they'd be targets again. Yes this does presuppose a Kostura that does more damage than SoaSE 1's, but that's up to the developers!
Your Alliance idea makes the least sense. Yes the Alliance want to work with TEC and Advent forces, but they're supposed to be co-equal. Building a terraformer to convert ideal Vasari (or Advent) worlds into ideal TEC worlds seems to be self sabotaging!!! And if the Alliance is selling out, then it's not a mighty empire guiding anything. How about instead a Babylon 5 type concept that allows for tech sharing between allies? If non-Alliance members are allied then relevant Enclave\Exodus\Primacy\Reborn\Wrath tech is shared amongst all allied faction. Alternatively create custom unlockable tech which empowers all the allied fleets e.g. Speed boost from Reborn for lighter materials, speed boost from Exodus due to better drives, Faster weapons from Wrath and Primacy, ... Techs should overlap so the more diversity in the allied forces, the more the power snowballs! If you have 1 ally from each faction on a 6 man team, then you get 6x the power. This should be designed to be incredibly unbalanced so as to force enemies to destroy the superstructure before the shared tech can be researched. This actually does suggest a way for your Enclave economic idea to work.
What if the Enclave superstructure were also an alliance option? Instead of simply granting a Tier 5 Pervasive Economy type personal economic boost, what if the player, and any allies gained something equivalent, but applied to all resources? And since it's about being an industrial, and economic juggernaut, what if there is a logistics boost so that the supply cap can be exceeded? Again the end result is intended to be highly unbalanced as it's intended to be game ending once it's a fully armed and operational ... oh wait, wrong universe!
Given resources are typically not the issue late game - usually it seems like there's tens of thousands of credits\metal\crystal, or even hundreds of thousands piling up, ways to spend would be more of an issue. Increasing logistics would both allow for more spending, and the larger fleet size would allow for snowballing. As a slight variant, what if titan and command ship caps were doubled? This would be consistent with the Enclave as an industrial juggernaut. Allowing for 2 titans, and 6 command ships per Enclave and allied player ... Allow this as a stepped option e.g. 1 at a time, very slowly constructed modules, and pressure would grow over time to enemies who didn't work together to wipe out the structure.
The Reborn's resurrection ability could likewise be extended to allies. This would then create a clear divide:
Enclave offer logistical and maybe economic boosts to snowball a victory - pseudo-Zerg rush, Alliance offer tech upgrades to snowball a victory - power overwhelming, well stronger, faster, tougher units anyway, and Reborn offer resurrection of any units killed within their superstructure's expanding AoE. These are all team support advantages, though the Alliance should offer the most as they are alliance focused.
Conversely the Primacy simply want to blow up enemy planets, the Wrath want to mind control enemy worlds, and the Exodus, well they'd wipe out fleets then move in to seize worlds. All very individual focused.
For multi-star maps, would each star need a starbase-wonder to apply the benefits? Primacy, Wrath, Exodus, and Reborn could all be range limited. Enclave and certainly the Alliance's advantages would not be.
The current factional victory options are TEC equipping Novalith cannons with Planet Cracker Warheads (
150,000,
40,000,
40,000,
30,
10,
10,
10) and wiping out 5 worlds, Advent equipping 3 command ships with Telepathic Amplifier (
30,000,
50,000,
75,000,
10,
10,
5) and having them sit around a star for 15 minutes, or Vasari equipping 3 command ships with Departure Supplies (
60,000,
48,000,
6,
6,
6,
6,
3) and likewise hanging around a star for 15 years er minutes before taking off on the next phase of the Dark Fleet's "ten-thousand year interstellar journey, allowing them to escape from war and the sinister unknown force that pursues them". Except weren't the Alliance trying to work with the TEC and Advent to avoid this? Are the Reborn also trying to get Yuri's Revenge? Isn't that the focus of the Wrath?
Diversification does seem like a good idea, but the current 3 options don't seem to quite match the alleged goals of the Enclave or Reborn, let alone the Alliance! Superstructures would also have the added advantage that they declare "we're here to stay" which would be consistent with the Alliance's goals as I understand them, and obviously the Enclave are all about digging in and protecting their territory. Reborn, they're more focused on cleaning up the Unity right?