So it's extremely important that they get an injunction that allows the cloud compute companies to continue to work them. I think they probably will, but it's really crazy that the government is actively trying to kill them off over this.
This would hand the federal govt to OpenAI and Google but would certainly be head-turning. Hard to say if it would pay off positively for them though.
The supply chain risk statute grants broad, largely unreviewable national security discretion and doesn't require the threat to originate from a foreign adversary.
Finally, the First Amendment claim faces the problem that the government was responding not to abstract speech but to a concrete refusal to provide services on the military's terms, which courts are unlikely to treat as protected expression warranting judicial override of procurement choices.
So it's not just that there's be a transfer of power to the executive (there is), there's also straight up executive overreach.
Now the main constraint on executive power seems to be due process and habeas corpus.