The most promising thing seems to be the API standard developed by the "Berlin Group" https://www.berlin-group.org/psd2-access-to-bank-accounts with quite a lot of banks being a member.
I quite liked the bunq API to work with (https://doc.bunq.com), but I wasn't really happy with their 7.99€/month pricing. In the past they also required a fixed IP, which wasn't really great for hobby projects.
A decent wrapper around multiple bank APIs seems to be figo (http://docs.figo.io/v3/index.html), the API looks good but I'm not sure about the pricing.