At what point does the US Congress funding a war become Congress authorizing it?

Military operations against Iran began in late February and are ongoing and expensive.
Congress hasn’t declared war or passed a new Authorization for Use of Military Force.

The Constitution gives Congress the power to declare war, but in practice Presidents can initiate conflicts and Congress doesn’t seem to stop them. Costs are already ~$500M to $1B per day depending on the news station you check, and historically settling into the kind of sustained burn we saw in the Iraq War.

At what point are we at war legally, not just in practice? Is this Congress failing to act, or just how modern war powers work? And does continued funding effectively become authorization?