Many US banks support OFX (though they may call it QFX, DirectConnect, or simply advertise Quicken support). The OFX spec is a bit of a pain, but there are a number of open-source libraries to query/parse it. I wrote one in Go: https://github.com/aclindsa/ofxgo

Many actually do have APIs, they're just poorly documented in public.

ledger-reconciler uses headless chrome underneath to screen-scrape all its information from banking/creditcard websites. That's how all the plugins hook into it.

It does not use any public or private banking APIs.

Hope that helps!