The screen shot you show on what would be updated ... that from the failed attempt or did you access that area again?
See the theme 'Essentials' ... that one I know could be massive.
What normally happens when continuing is that the new plugin code is downloaded to your server, then unzipped ... actually re-creating the directories it removed for the various plugins ... in theme an essentials directory ... in mod the mod_attenance etc.
Know for a fact the essentials theme is one of those massive updates. Moodle once downloading all those files, will/should take you to a screen that ask you to 'update' ... that's when the database becomes involved.
Once by that, moodle then takes one to a screen that shows *all* the settings for *all* the plugins ... *all* the plugins ... and that's where it might hickup. Too much to display ... times out/errors out ... (has to do with settings for PHP ... time for a script to run, memory a script can consume, etc. and some of those you might not be able to tweak upwards).
That's why, when there are many plugins to update, I don't update them all ... the ones I know are massive ... like Essentials ... I'll save to update individually.
The error, however, it reports is a 'bug' that was reported and fixed.
'Overwriting' should never be done ... replacing yes ... *** but *** what you are proposing is taking what is old code for those plugins mixed in with new core code ... which now may/may not (more than likely may not) match all the versioning information in the database for those plugins.
If you try the above, do create a backup of the code/db before attempting ... if that fails at least you can put it back to the confused/errored state to move forward with upgrading to a higher version.
Since you don't have backups taken right before you updated the plugins (shame on you), the two options you have are: restore the backups you have, even if it means loosing data/days ... or upgrade to a higher version of Moodle that fixed the issue.
The tracker https://tracker.moodle.org/browse/MDL-57283
says fixed versions 3.2.1 and up. So what version of Moodle do you have? ... a 3.2.0+?
Viewing the version.php file in moodle code will tell you.
If my thought process is faulty and any others spot it ... please jump in here and correct! ;)
While it's reported that 3.2 can run under PHP 7.1, I thought, I wonder if you've not discovered a regression with 3.2.lowest and PHP 7.1? (lucky you, huh! :\)
'spirit of sharing', Ken