S.O.S.: drupal 7 site broken after failed update to 7.56, full restore from backup fails

I have tried today to update drupal core to 7.65 on my 7.54 site.

Before update, I did a full backup using the module "backup & migrate".

Then I followed the update instructions.
It seemed to work (version 7.56 has no DB updates, right ??).
The public section of the site is displaying ok.

But then I noticed ckeditor was not loading anymore on text fields.

And some buttons on node edit forms give the following AJAX error:

An error occurred while attempting to process /file/ajax/field_featured_image/und/0/form-Id344TP4hl9hkHa1hmIC9FotQZaqn06r7HiAmKs9_zw: Cannot read property 'replace' of undefined

I thought, ok, the update has gone wrong.

Then I first restored from backup.
To my amazement, the errors were still there and the site status report did still give 7.56 as the installed version !?!

Then I deleted all files and dropped all DB tables and restored them manually from the backup files.
Luckily, I still got a coipy of the settings.php file somewhere because apparently the module "backup & migrate" has problems in English comprehension what "entire site" means...

Well, this time the site report gives 7.54 as a version, but the glitches are still there.
How is this possible??

I deleted all possible caches on the server and in the browser, I'm at the end of my knowledge.

Please help me get my site back up.