Actual budget is the closest thing to YNAB4 that I’ve tried so far. The API enables you to import bank transactions automatically as well so it’s actually more convenient. Responsive enough as a web app on mobile but lacking the depth of reports and overall slickness of YNAB currently.

Clapshot I think it’s called. There’s also Kollaborate.tv, far more features but its selfhosted option is paid. Only two options I’ve found so far.