Still Another update is currently in progress by updating WordPress 5.3

Something went wrong while you were updating your website.

Two solutions :

1/ Install and activate this plugin : Fix Another Update In Progress. In your settings, simply click on “Fix Another Update In Progress” and the plugin is going to fix your problem in a few seconds.

(Before using following solution, backup of your website.)
2/ Manually : In order to fix the problem manually, you can simply locate (using you ftp client) your upgrade folder and delete it. The upgrade folder is located under the wp-content folder (dont suppress this one !).

If the problem is persisting, try to locate (using your ftp client) a .maintenance file at the root of your server and delete it.