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If US Congress decides to spend 1 billion USD on weapons for Ukraine, they will not wire 1 billion USD to a bank account in Ukraine.

The US government will give > 900 million USD to US companies that build weapons in factories in the US, employing US workers who spend their salary in the US economy, boosting it.

The US government will also spend a couple million USD to transport the weapons produced in the US to Ukraine.

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Russia is also employing Russians to manufacture arms who spend their salary in the Russian economy. The important thing is how much value in infrastructure the government gets for the keynsian boost it's giving, since wars generally last until one side runs out of credit.

The apocryphal calculus in Afghanistan was a 100 000$ US Stinger missile was generally worth one 2 000 000$ soviet helicopter. I'm sure there are US defense systems that would be similarly good tradeoffs, but I'm also sure there are difficulties in spending billions at a time on anything cost-effective. It's hard to spend large amounts of capital effectively and all that.

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