Hi Issa,
What an unfortunate situation 
Sorry for replying in English, my French is not good enough.
Transfering all settings can be done by making a backup at home, copying the backups to removable storage, take the storage to a place where you can upload it to your temporary VPS.
You can upload the backups before running postinstall on the new server, move them to /home/yunohost.backup/archives (a user with SSH access most probably does not have write access to that directory, so you’d need two steps), and use the system backup to reconfigure your domains and users:
$ sudo yunohost backup restore name_of_system_backup
After that you’d restore the app specific backups (if any).
There are similar threads about moving to another server on the forum, usually with people still having internet access. One where I posted earlier in the context of migrating to another homeserver, another by @Tio using Borg (which is not a convenient option at this moment in your case, but could give some inspiration)
Some things to keep in mind:
- Storage size of the VPS: usable space might be a bit less than technical space. If your current server is 19GB, you should get away with a 20GB VPS, but your current server it is 19.5GB, I’d opt for a step larger then 20GB. I guess your homeserver has much more space; if you only need emails for now, I imagine 10 GB for the whole server would be enough.
- Early in the process, but certainly before restoring backups: install a terminal multiplexer such as
tmuxorscreento keep the running processes active when your connection drops.screen -DRreattaches to a running session (or starts a new one), so you can continue your activity where you left. - To move back to your homeserver, you can backup your emails, download the backup to your server, and restore it. Another option would be to use mbsync/isync to synchronize the mailboxes.
Good luck!