“rest_not_logged_in” 401 on connect

If a site connected with an Application Password returns 401 rest_not_logged_in even though the username and password are correct, your host is almost certainly stripping the Authorization header.

1. 1The quickest fix: switch the site to the WordPress plugin. Download it from the WordPress card on Settings → Connections → Connect CMS, upload it and activate it. It doesn't use the Authorization header, so the 401 goes away.
2. 2To keep the Application Password instead, confirm the account is an Administrator or Editor (a Subscriber gives 403, not 401).
3. 3Then follow “Fix the WordPress REST API Authorization header” (CGIPassAuth, .htaccess, disabling the CDN).