The actual study seems to be unavailable and the article itself (from a right-wing rag) is so low on details that it is hard to say if the actual study makes more sense (but I am doubtful as this “institute” is just a shitty big-industry lobby organisation).
But according to the article they compared two imaginary simulations for 2023, and the result was 4.5% points less GDP. Besides the fact that this institute is not exactly known for their high quality economic simulations, this also makes little sense. As it currently does not look like there will be a deep recession in 2023, this can only mean the 4.5% are mostly less positive growth in their simulation. As Germany didn’t have such strong economic growth in many years this makes their “no war” simulation seem hilariously optimistic, and thus their “loss” calculation likely a huge over-estimate.
Also less positive growth is not the same at all as “costing” something. It just means that you don’t increase your earnings as much.