The single major issue I have with this DLC is that the Imperial Spire fleet doesn't share vision with you so that you can see all the pretty fireworks as they rampage throughout the galaxy. The alternative win condition would be a lot more fun to watch if you could reliably watch it.
Fallen Spire ships are all the same ship. They all have the same gun, move at the same speed, and have the same HP/shield to DPS and cost ratios. A frigate is exactly 1/4 of a cruiser, a destroyer is exactly 1/2 of a cruiser. I get that spire fleets have to be slow because they're so powerful, and it's convenient for them to all have exactly the same speed so they don't get separated, but maybe the frigates and destroyers could have different guns? Instead of the coilgun, frigates could have the spire multi-shot laser pulse weapons so they're better at clearing out massive swarms of smaller ships, and destroyers could have an infinite-range single-target spire railgun so they can pick off things the slow spire ships can't catch. Normally you'd fill these roles with human ships escorting your spire fleet, but you could instead choose to spend sockets on covering for your spire fleet's weaknesses rather than on economy or defensive structures.
The AI taking shards and relics isn't very impactful. Past the earlygame you can generally ignore it; the AI gets a single mk1 cruiser or battleship that's easily taken out by human ships that can punch up (eyebots, gunbots, etc.), your own much higher mark spire ships, or the defenses you've already built that are capable of killing exo-war units. The mark level of the spire ship the AI gets should at least match the AI mark level.
The interactions with the minor factions are great. I like making the game messy and having a lot of minor factions running around, and I really appreciate how most minor factions have their own unique interaction with the Fallen Spire.
I love all the new turrets. They integrate so well into the base game that sometimes it's hard to tell which ones are DLC-added; I almost forgot to mention how much I like them because I nearly forgot they were part of the DLC.