The Dashboard says WordPress still asks search engines not to index my site

WordPress has a setting of its own under Settings → Reading, Discourage search engines from indexing this site. It is often ticked while a site is built and then forgotten. Once your site is open and it is still ticked, the Dashboard says so. Open means the mode is off, the shop is closed for orders, or Apply to puts your page on some pages only; a page applied everywhere with a page or two left open under Exclude still covers your site. While your page is up with a switch-off time, the note waits for the switch-off, and the status line says what WordPress will still ask.

• Let search engines index it unticks it, as saving Settings → Reading would, and empties the page caches the plugin knows, because the pages they kept still ask not to be indexed.
• Keep it hidden leaves it ticked, for a site you want kept out of search engines, and puts the note away until your coming soon page is next up. A maintenance window or a shop closed for orders does not bring it back.

If the note also names a robots.txt file, a file in your site's folder asks every search engine to keep off every page. A file with a group of its own that lets one search engine in is not named. The plugin never edits that file: ask your host or developer, who may have put it there for a staging copy.

Nothing is said on a site WordPress knows as a staging, development or local copy, or while a site privacy plugin controls that setting. The note reports only what the setting and the file ask for; how soon a search engine visits again is up to the search engine.