I am perfectly fine with the Athena being a planet shattering beast of a ship with one or more novaliths on board.
As for the Coalescence (what I'll call the Advent titan until I hear otherwise), it would be awesome if it could just mind control entire freaking planets. You think Domination is impressive? You think Repulse is powerful? Just wait until you get all those psitegrate in the same ship focused on the same target. If you want it as your own, it is yours. If you want to annihilate it, it simply goes away at .99999999c via a telekinetic burst.
Lacking a cool name for the Vasari one, but anyways... This thing really needs to be in complete control of phase space. You want to create a phase node? Done. You want to phase out the enemy fleet? Done. You want to phase out the freaking enemy gravity well? Done. You want to phase out the front half of an enemy starbase, utterly destroying it? Done. You want to positively rend all ships in the gravity well with a phase shockwave? Done.
I mean, As awesome as these things will be combat wise, think of the sheer unspeakable power of their abilities! I mean, come on! The TEC should be able to raze planets to the mantle. The Advent should be able to dominate entire fleets or planets. The Vasari should be able to simply delete things from the universe. I mean, at this scale of power, you have death stars. They have lots and lots of small guns, but if you tick off their captain... Your entire empire will quake in fear of the repercussions.