Hi @keverets
Before anything save all your backups outside yunohost to be able to import them.
YNH 13 is still beta you so if you didn’t do a backup prior upgrade, this will be complicated ( Backup restore silently fails in YunoHost 13 - #6 by wbk ).
It is possible to reinstall a yunohost system by installing it ( Install on... | Yunohost ) then restoring system backup ( with core ) that was done for that YNH 12 version.
I assume here backup was a full one and that all files were included, it might occurs that some applications don’t have a working backup/restore system. If you have applications with a level below 6 and/or did install through url directly, anything can break.
If you want us (ie yunohost community of contributors) to find out how to fix your current installation, all yunopaste logs of failing installation are required, there are far too many variables that a general answer is not possible, and even with logs it is not sure we will have time and to dig in it. There is a matrix support channel too.