Migrating to HTTPS only, most media library links need updating?

Here’s what I did (step 3 should probably solve your problem):

1. Update .htaccess File

Add the following to the .htaccess file:

RewriteEngine On
RewriteCond %{HTTPS} off
RewriteRule (.*) https://%{SERVER_NAME}/$1 [R,L]

2. Update WordPress Site URL

Navigated to Settings > General and update the WordPress Address (URL) and Site Address (URL) to https.

3. Update Old http URLs

1. Install the plugin Velvet Blues Update URLs
2. Go to Tools > Update URLs
3. Enter Old and New URL, e.g. Old: http://www.example.com and New: https://www.example.com
4. Check all checkboxes and click Update URLs NOW
5. Repeat steps 3-4 but remove “www” this time, e.g. http://example.com and New: https://example.com