Is the practical outcome much different? I doubt they'll get contracts either way, so the labelling was just a formality.
If anything it seems the label was just intended to give a veneer of legitimacy to the admin by using an existing mechanism and terminology, rather than saying "we're going to block your access because we feel like it".
I believe designating an entity a supply chain risk has far deeper implications than the DoD avoiding that entity, and goes as far as a lawful prohibition for any contractor of the USG being also prohibited from using or working with the entity so designated. Ironically enough, if the comments in this discussion are true that Palantír uses Claude, Palantír would've also been prohibited as well.
It's a strong signal that the government cannot strong arm privates.
The Supply Chain Risk label requires every single company in the supply chain of a product or service provided to the US Government to either drop Anthropic or get dropped themselves. This is not just suppliers, but also includes suppliers of suppliers all the way down. This is a much larger chunk of the economy (approaching 100%) than the Pentagon/DOW.
The point of the supply chain risk designation was not just to have the DoD stop using Anthropic (they could have done that by just cancelling the contract). Their intended effect was to force every company that sells to the US government, no matter how indirectly, to not use Anthropic in any way, which would effectively destroy them because almost every company is in the supply chain (for example my company is https://calaveras.ai/ because we sell to AI companies who in turn sell to DoD).