What's missing is what is called a 'dependency' and is part of Moodle 3.4.x core code. The question that comes to my mind is ... why is a part of core code missing? Might stem from how one installed ... or even tinkering where one shouldn't tinkering. Dunno. No Vulcan Mind Meld possible here! Image may be NSFW.
Clik here to view.
I see a 'upload zip' link ... am thinking that to repair this you could:
1. download the 3.4 code zip.
https://download.moodle.org/releases/security/
2. unzip it locally.
3. find the moodle/admin/tool/mobile directory in the unzipped folders.
4. zip just that directory ... the 'mobile'.
5. return to the area you show and upload the zip you created.
The question about upgrading to 3.5 ... and if all that content you've created will still be there ... should, because much of the info is actually in the DB and if one did upload files, those files are kept in moodledata. So replacing the code directory with a 3.5.x copy and copying config.php file from the current site into the new 3.5 code (plus any addon code installed in the 3.4), should trigger an upgrade.
Before you do that, however, please know how to do a site backup ... code directory, db dump, and archive of moodle data. As well as read:
https://docs.moodle.org/35/en/Upgrading
especially the part about requirements.
'spirit of sharing', Ken
