As soon a country agrees to enter a conflict on a side, which the original axes declare to be a war, it's at war. You can tell the media whatever you want of course.

The US didn’t declare war since WW2 because such a declaration would give the president disruptive powers (such as the power to seize factories).

In fact, after Vietnam war congress specifically created a law to restrict hostilities without congress approval to up to 60 days, which is what the current (and prior) administrations are acting on.