Hi Emma,
I don't think, you'll find this feature anywhere in the Google Ads API. On the other hand: the status "Limited by budget" you'll see on the website is flawed in itself (it seems to last for 7 days, no matter how the actual ad spend is on the following days).
What we do is to check the cost against the budget amount. However, that's pretty tricky too, because you'll have to check for budget changes (amount and allocations), associated campaigns, days in the month, paused and/or reactivated campaigns, ad schedules etc. - and you'll have to guess or test how Google calculates with these parameters (e.g. if the campaigns only run 5 days a week or only two hours on the weekend etc).
Regards
Mat