My wife and I tried a number of apps and settled on YNAB. We've been using it for a year now and the app is incredibly helpful. Fair warning, the learning curve is a little steep.
Fortunately, it supports syncing with the small credit union we belong to. It does NOT support some of our accounts like our retirement accounts, some credit cards like Apple and Sam's Club, but it supports enough to be convenient.
YNAB does have an API https://api.youneedabudget.com/
My wife and I are considering switching banks to have more reliable integration with YNAB.