The media file item (really, a post type), has the URL of the media item as part of it’s data. So if you upload a media item when your site is at http:, then the URL of the item is stored as one of the meta values of the item. (It will be stored as http://www.example.com/wp-content/uploads/whatever.jpg , for example.)
Since the URL is part of the stored data for the media item, then you need to use a Search and Replace plugin (my favorite is “Better Search and Replace”) to replace all instances of http://www.example.com with https://www.example.com . (Backing up the database first, of course.)
That is not absolutely required. If you are using a standard redirect in your htaccess file to redirect all http requests to https, then the https URL will be served up by your server. A sample htaccess that would do this is this one; you should add that to your existing htaccess file at the top (before the ‘Begin WordPress’ lines).
RewriteEngine On
RewriteCond %{HTTPS} off
RewriteRule ^(.*)$ https://%{HTTP_HOST}%{REQUEST_URI} [L,R=301]
It may be that URLs in your generated page will still have the http, instead of https, when you use the htaccess rule to rewrite the request. But using a Search/Replace plugin will fix the problem.