The victor writes history. Psi-Corps may have considered it a war, But afterwards EA tuned it down into a crisis.
Crusade ~ Valued Judgements (unfilmed, but scripted, I count this as Canon):
Bester: It wasn't a crisis, it was a war
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Also, before that, bester believed in a coming war between Teeps and mundanes. I believe he was gathering his forces for that. That means he was recruiting people, but also he'd need more than a small fighter squadren to take on all of EA. My campaign will be based on that belief, I don't ask that you also follow them.
All I ask is that someone does Psi-Corps reskins for the Hyperion, Midwinter, Nova, Omega, Poseidon and Warlock, and that someone Models the Carrier seen in Epiphanies.
As to where they got them - ships officially listed as MIA or destroyed that have been recovered, ships that were stolen - though someone else was blamed (ie Raiders) - by the Corps. And various other methods.
Oh I agree that they will not have as many ships as the EA, but when modified to use Shadow weapons and/or combined with the Psi factor that can be quite devestating.
And as for Man power:
1 Automation
2 Mind Slaves Mentally controlled people like Garibaldi was in S4
3Mercenaries