WordPress provides the basic functions for the website, plugins are used to supplement them.
The message from Site Health means that you do not have minor WordPress updates installed, e.g. from 6.2 to 6.2.1. This makes little sense. Probably this was set by a plugin you use or entered in the wp-config.php.
Why you can not install updates, however, is quite interesting. None of what you described should affect that. Is there enough free space in your hosting? Can you look in the error log on the hosting to see if there are any entries for this? The support from the hoster can help with this.
Thank you very much for your comments.
As for the minor WordPress updates, where and how can I confirm it? I look at the dashboard to find 6.2 only.
In my hosting, the disk space is ca.90% free, and the number of files is just about 3% of the maximum limit.
I set the debug “true” as my server vendor recommended, however, no debug messages appeared on the screen when I updated plugins successfully or in vain. Am I looking at wrong places?
WordPress 6.2 is the latest version. There are currently no updates for it.
Activate the debug log as described here: https://ww.wp.xz.cn/documentation/article/debugging-in-wordpress/
Invalidating the latest-updated plugin resolved the issue. It was simple as that.