I finally asked the Discourse team for confirmation that SSH access is required to upgrade this server. I’m posting this here so you know where we stand at, and give the community a chance to solve this altogether. @mxb, please have a look, I hope you’re well and available enough to spend the little bit of time unclogging this situation. Best wishes.
I tried to change email settings, only to realize that the SMTP settings are set to environment variables, hence not updatable. Again, without a short intervention by @mxb, we cannot send email (including registration, password recovery, admin creation, even backups). The intervention is easy and straightforward, but only someone with root access can do it.