Maybe someone will find this a useful tip for exactly that - finding out which Moodle version you''re using if you're not an admin.
Non-admins have no access to the notifications panel and the site administration.
Of course you can always try to message / email the admin of the site and ask, but - as long as you teach in at least one course on the site - there is a way to get the full info directly. The trick is to backup any activity inside a course in which you are teacher. Then download the backup mbz file, open it as an ordinary archive (which it is - it's a zip file after all), and then open the moodle_backup.xml file. You should find the "moodle_version" and "moodle_release" tags with all the information near the top.
I thought I'd share this tip, maybe there are other ways, but I've just recently helped myself discover the Moodle version on a site I was teaching in.
Przemek