The easiest method is to use the MediaRecorder API to capture a MediaStream, to which your audio graph is connected to. This will get you a recording, typically in Opus (unless you want Vorbis, but I don't recommend it), and you can either stream the data from the MediaRecorder as its emitted, or let it record a whole "file" which you upload afterwards.
As of how you store it... you can store it however you want. That's really an unanswerable question without knowing what your requirements are. Sure, I suppose you could jam all your binary data in your database, and there are rare use cases where this is useful... but usually you'll want to keep this blobs somewhere else and reference them from your database.
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