Finding version of Moodle ... Site Admin Menu, Server, Notifications ... version is at the bottom.
There is no Admin link to list all backups. Backups are found in the individual courses and in some cases where teacher has made a backup, those are in the teacher's private files area in each course. Think there have been suggestions made in the past programming something for the Admin user what would allow seeing all backups, but no movement in that area.
Can only guess cause I've never seen/read any explanations from Moodle HQ, but ... as a long time Admin person of several Moodles, there was a change in how much 'power' an Admin user should have in a Moodle - in particular, related to backups of courses. Remember, Moodle is programmed in a fashion to *try* to be everything to everybody ... but mostly for colleges/uni's ... sites with multiple courses, teachers, and students.
In the past, each course had an ID numbered directory in moodledata and in there teacher as well as admin person could see files and backups by humanly recognizable names. Problem ... teacher taught more than one course, teacher had to upload docs/files to each course ... like an intro video ... which meant, if teacher taught 4 courses, that video would have to be upload 4 times ... thus taking up 4 times the space.
Beginning version 2 of Moodle ... major change ... all files are uploaded to moodledata/filedir but are no longer visible by humanly recognizable names but rather a contenthash value which is created when file is uploaded (a lot more technical info concerning that). This system allows that teacher to upload the video just once yet be able to link to the video in all 4 courses.
As with anything ... there is yin/yang ...
Backup files (.mbz's) are just like any other files when it comes to storage under the new system.
One will find many who recommend installation of a plugin that will allow the admin to create a report showing all backups contained in moodledata/filedir.
One will find many who recommend using automated backups to a designated directory that admin user (server admin) creates outside of moodledata/filedir in order to be able to find a backup by humanly recognizable names ... and through other apps ... like FileZilla ... be able to download them.
Since there is greater interest in privacy today (GDPR), that also gets into files ... especially backup files because they normally contain all the students work ... as well as personal information.
BTW, a backup file (with mbz extension) is no longer a zip with a different extension, but a gzipped file (Google that) for better compression in creating backups. Downloaded and un-archived without restoring to a moodle is an 'adventure' if one expects to see humanly recognizable file names/info.
IMHO, even though it has quirks and room for some improvement, the new file system is overall better than old. It just takes some getting used to ... and I realize no one likes change, but change is the only constant!
'spirit of sharing', Ken