How to manage project revaluation

We have an issue with the projects budgetary control scenario that we would like to share. Our Ledger currency is ILS and the project currency is USD

Let's say we have a budget for project1 for 2000$ for 2023. The currency conversion rate in Jan is 3 so from GL perspective we expect to have expenses for the project1 of 6000 ILS

Now, on 8/23 someone purchased an Item for 2000$. The currency rate now is 3.5 so in GL we get 7000 ILS expense   

From project perspective it looks fine but from GL respective we are 1000 ILS over budget

Two questions:

1. Can we set the budget control (Project) to be in a different currency than the project currency? In the example above the control will be in ILS although the project currency is USD