It's not a war even if Congress approves it. It's still just "an exercise of the War Powers Act", which is not technically the same thing.
To actually be a war Congress has to declare war. But they passed the War Powers Act so that they wouldn't have to do that.
In theory, the War Powers Act is limited to 60-90 days unless Congress approves funding. Which they may -- a bill to refuse funding failed. Which isn't the same thing, but even if they can't pass the authorization, it's not clear if that actually matters to anybody.
I think the country isn't officially at war without an act of congress, but whether a conflict is a war is probably a property of the conflict and not government declarations of the beligerants or the legallity of their participation.
Anyway, the Department of Whatever its name is needs money.
To actually be a war Congress has to declare war. But they passed the War Powers Act so that they wouldn't have to do that.
In theory, the War Powers Act is limited to 60-90 days unless Congress approves funding. Which they may -- a bill to refuse funding failed. Which isn't the same thing, but even if they can't pass the authorization, it's not clear if that actually matters to anybody.