But the language in the stay shows very clearly that the court is likely to ultimately rule against the government.

People often don't realize this because defendants like to emphasize that it's not a final decision. The reality is that any time a temporary injunction is granted it's a sign the court will rule in favor of the plaintiff. Courts weigh several factors when deciding whether to grant a temporary injunction, and one of those factors is if they think the plaintiff will prevail on the merits. It's technically not a judgment on the merits, but it kind of is in reality.