In your domain model your Budget/Localamount has a microflow Calc_LocalAmount. That will look something like this:
The retrieve is over association $Invoice/Invoice_Currency.
The CreateDecimal is:
if($Invoice/Amount!=empty and $Currency!=empty)
then $Invoice/Amount*$Currency/ConversionRate
else 0
On the budget screen, change your LocalCurrency-dropdown to a Reference- Selector. As On-change-action of that selector save set Save, with ClosePage to No.
See this example page: https://forumquestions-sandbox.mxapps.io/p/fq101233. Whenever you change the selected local currency, the object gets saved and the AmountInLocalCurrency gets recalculated.
This is all happening server-side. More efficient and performant would be to do this client-side, setting the onchange to trigger a nanoflow, but that’s another story...