Sometimes Joomla 4 shows there is an update for the "Installer - Install from Web" extension, but when you try to update it you end up getting a "PLG_INSTALLER_WEBINSTALLER_ERROR_PLUGIN_INCLUDED_IN_CORE" error.
This video shows a fix for this issue.
The full text of the error message that you get on the screen Extension Update:
Custom install routine failure. Before updating ensure that the update is compatible with your Joomla! installation. You are strongly advised to make a backup of your site's files and database before you start updating. × danger Error updating plugin.