When is zakat due on gold bought in installments, bearing in mind that the first bar was bought in 10/2021 and the last bar in 5/2022, and the total weight reached the nisab in 1/2022?

Zakat is not obligatory on gold and cash unless a full year (Hijri year) has passed since they reached the Nisab.

Cash can be added to gold to complete the Nisab. If their combined value reaches the Nisab of either currency (gold or silver), Zakat becomes obligatory on both at a rate of 2.5%, even if neither of them individually reached the Nisab.