Steps to reproduce the issue

Fortunately, this problem did not repeat itself after my site was recovered. But this is what happened:
I restored my site from an earlier backup and found 8 extension updates listed.
I began with updating the Akeeba backup. I immediately got an error message:
0 Class "Joomla\Plugin\Installer\Jce\Extension\Jce" not found
Strange as it was not related to the Akeeba extension.
I then found that any attempt to update any extension produced the same result.

Expected result

I would have expected the updates to be carried out as normal.

Actual result

Error message 0 Class "Joomla\Plugin\Installer\Jce\Extension\Jce" not found

System information (as much as possible)

Joomla! 4.4.5 Stable [ Pamoja ] 28-May-2024 16:00 GMT
PHP 8.1.28

Additional comments

In the end, I uninstalled the JCE installer plugin and reinstalled the full JCE editor extension, which resolved the problem.
It would appear that on updating an extension, sometimes the files are not copied. In this case, this led to my site breaking since the plugin file Joomla! tried to load was no longer there.
For obvious reasons, I have not tried to reproduce this by experimenting with various permutations of updates.