Here's Atlas's fleet losses as things stand:
1 / 1 Ark Mechanicus [100% losses]
11 / 40 Battleships (7 / 26 daemon) [27.5% losses]
19 / 60 Grand Cruiser Squadrons (8 / 30 daemon) [31.67% (26.67%) losses]
68 / 90 Heavy Cruiser Squadrons (16 / 30 daemon) [75.55% (53.33%) losses]
11 / 30 Battlecruiser Squadrons (3 / 7 daemon) [36.67% (48.86%) losses]
88.75 / 90 Cruiser Squadrons (14.75 / 15 daemon) [98.61% (98.33%) losses]
126 / 300 Frigate Flotillas [42% losses]
92 / 125 Destroyer Flotillas [73.6% losses]
5 / 70 Raider Flotillas [7.14% losses]
And here's our Muspelheim losses:
0 / 1 Dreadnoughts
0 / 2 Command Battleships
0 / 12 Armoured Battleships
6 / 24 Grand Cruiser Squadrons [25% losses]
12 / 24 Heavy Cruiser Squadrons [50% losses]
12 / 12 Armoured Cruiser Squadrons [100% losses]
23.7 / 24 Escort Cruiser Squadrons [98.75% losses]
23.8 / 24 Frigate Flotillas [99.17% losses
0 / 11 Nomad Cities
0 / 9 Orbital Cities
17 / 100 Defense Stations [17% losses]
479 / 500 Heavy Weapons Platforms [95.8% losses]
2464 / 2500 Weapons Platforms [98.56% losses]
1.75 / 2 Defence Cruiser Squadrons [87.5% losses]
3.98 / 4 Defence Monitor Flotillas [99.5% losses]
Losses on our end look pretty bad, but given they've only got 24 hours until "And Suddenly Eldar" and they can't seriously damage the Nomad Cities or Orbital Cities if they want to capture tech it's worse for them. Especially considering the number of Defence Stations left, which IIRC each have two Super Lances that they can use to begin absolutely tearing into the remaining enemy fleet. Plus our losses elsewhere were pretty light.
Now that we won a crushing victory, could we use this opportunity to sneak Men of Stone into the Imperial Trust? I'm thinking we could get the Security Council & Mechanicus to buy Muspelheim's "advanced targeting auspexes" and integrate them into their warships & defences. Centuries of dependable usage could help soften the blow of the reveal.
Not happening. The conservatives would find out that they're AIs pretty much immediately and likely revolt. No need to rock the boat on that front, especially with the xenotech issue likely to come up from the tech trade.