In Germany, we have HBCI/FinTS, it's basically a standardised protocol to do "home-banking", and it works really well. I use an open source Java app, Hibiscus [0], and it connects to all my accounts and downloads the transactions. I can also make transfers in the software and they're pushed to the respective banks.
It's almost what I imagine client-server Open Banking could have been.
There's also the EBICS protocol, but that is more for B2B, server-server communication I believe.