oh, I see. By "old interface" I was referring to the Vector legacy (2010) skin where none of the search boxes work for me (the browser console shows the mixed content error). With the new Vector (2022) skin, I can use the search box at the top to look for items, but the search box or input box, to look for and add statements doesn't work.

Yes, I've been using the latest release tags/wmde.20 following these instructions https://www.mediawiki.org/wiki/Wikibase/Docker (I'm not sure about what you mean by template)
I've tried changing the values of $wgServer to a protocol-relative URL and $wgCanonicalServer to an absolute URL in LocalSettings.php but it didn't change much (Running a mixed-protocol wiki - https://www.mediawiki.org/wiki/Manual:HTTPS)

with these changes, QS authentication and the search bar works fine with the new wikibase interface, but the input box to add statements and the search bar in the old interface trigger this error