I am wondering if there are any digital libraries offering search by example for audio files, e.g. upload part of a music file and the digital library recognizes the song and provides me information about it? So, something similar to Shazam, but directly integrated in a digital library.
I don't know if you consider it a "digital library", but the MusicBrainz project have a sister service called AcoustID which uses an audio fingerprint to look up metadata for a given audio file. The tooling and data around AcoustID is opensource. So if you are building a digital library service you could theoretically integrate into your applications. If you are new to MusicBrainz it has been around for 12 years now, and its data is widely used and supported by organizations like the BBC, LastFM and Google.