[Bug]Adding a password will be indexed by search engines

If you want to exclude these pages from indexing, you should use an SEO plugin to set the robots value to noindex. You can find examples of SEO plugins here: https://wordpress.org/plugins/tags/seo/

Then everything is correct on the website (and WordPress) side. You would have to ask Google why the site is indexed. A look in their Search Console could help. Otherwise, ask their community what it could be: https://support.google.com/webmasters/community?hl=en