> does anybody have more information on what that URL is for?

Many years ago, Google Search existed only on http:// and schools used filters to block searches that they didn't like. Then Google shipped https:// for search on www.google.com, upset the schools because they could no longer block just some searches, then moved encrypted search to encrypted.google.com so that the entire domain could be blocked: https://cloud.googleblog.com/2010/06/an-update-on-encrypted-...