Just a couple thoughts on this. Instead of the general upgrade you have for the Deliverance engine, have culture from DE shots be able to decrease a planets allegiance faster (ie .10 instead of .07). With all the buffs/debuffs/etc you have between your general upgrade and your proposed faction upgrades it gets very complicated and a little OP imo.

Similarly, the general upgrade to the Kostura Cannon seems OP. Half shields and 0 AM means anything in that grav well will get eaten alive, especially with a Titan in play. I do like the bit about the mines though.

I like what you suggest for the TEC, I do think that since the Loyalists are able to build so many more Novaliths than the Rebels that this is a little OP. Maybe just the passive regen part.

It occurs to me that maybe you mean for the faction specific upgrades to replace the vanilla upgrade. If so, here's my rundown:

TEC Rebels: ok

TEC Loyalists: OP since they can build so many Novaliths

TEC Vanilla: I like this

Advent Rebels: Ok but I think you're assuming each race will have an offensive/defensive faction. Seems to me that the Advent Loyalists would be the more aggressive of the two, maybe switch them. A little OP but not much.

Advent Loyalists: Id suggest something that buffs their in-culture bonuses even more. Higher shield regen or something

Advent Vanilla: have culture from DE shots be able to decrease a planets allegiance faster (ie .10 instead of .07)

Vasari Rebels: I like this

Vasari Loyalists: 25/30 secs instead of 45. Other than that, good.

Vasari Vanilla: OP. Maybe 1/2 AM, disable passive shield regen for 45 seconds, mines visible.

Just my thoughts, I do like the idea of giving super weapons more of a reason to be built. These upgrades would probably require a cost increase as well to try to keep it somewhat balanced.

I'm personally okay with super weapons unbalancing the game if their cost is reasonably high enough. You could think of their upgrade cost as buying a "non-guaranteed win condition".

The only super weapon that needs help is the Deliverance Engine IMO.

The Novalith's planet damage is reasonably countered by Starbases, but in just one novalith blast it does so much damage to your opponent's economy that it might pay for itself. The -40% population and -100% trade debuff last an insane amount of time: 1800 seconds, or a full half hour. Ignoring the trade effect (which can often be more effective), lets say you novalith your opponent's homeworld making 15 credits from population taxes. The -40% population debuff means it is now making 9 credits per second, a loss of 6 credits per second. 6 * 1800 = 10,800 credits you've denied to your opponent over that half an hour. Factor in the trade income you've also halved and the fact one novalith can keep 5 or 6 planets at a time under this economic penalty, its pretty substantial. The fact that you can also use it to completely destroy unprepared enemies and force your opponents to waste a starbase slot and resources on axillary government is a bonus.

The worth of the Kostura is a bit harder to calculate, but the ability to shut down repair platforms and Vasari hangars should not be underestimated, and can really make a planetary assault a lot easier. But of course the main bonus is that phase node it creates, which can range from worthless on small maps to utterly invaluable as you render front line fortifications useless and can even outmaneuver your opponents fleet in their own territory if you have enough of them. Unlike the other two there's nothing you can really do to mitigate their effects either, you just have to take the full force of whatever your opponent is going to send at you, at whatever location he chooses.

The Deliverance engine suffers as being both the hardest super weapon to deploy (maxing out culture is both expensive and unlike the TEC missile line not very useful) and a lack luster effect. It was worse before Entrenchment, as its culture effect can be completely negated by enough culture centers, and you need several engines to cause allegiance to get low enough to over through  a planet anyways. At best you'll do minor economic damage due to lower allegiance. The +25% damage output buff it got is substantially more useful and its a bonus that can make a late game Advent fleet utterly terrifying with both extra damage and shield mitigation, but most games are settled by this point and the resources you need to get it are not really worth the cost in most cases. Its certainly does not give the same bonuses of the other two that's for sure.

oh ok lol

Well for simplicity I kept it to one tech added to each faction or 1 tech per race. Using a crew slot is a good way to balance how many are in play.