Moodle in English: Upgrading from 3.4 to 3.9
Warning ... opinionated response follows ... nothing personal! Since you are IT, a question ... is platform Linux? Is hosting on a shared plan? Do you suffer from CLAS (command line avoidance syndrome)? Migrating the entire site is possible ... but a big factor is question 2 above. By far, the eaiest way to march a moodle (which is what you are doing) is best done via git (command line only). The first hop in the march is the time to move site under git, but that depends upon not only ...
Source: moodle.org