Please help us help you and fill where relevant:
Your LimeSurvey version: [3.6.7]
Own server or LimeSurvey hosting: own Server
Survey theme/template:
==================
After a (manual) update from 5.6.8 to 3.6.7, the survey templates are not available, meaning that I can't load existing surveys or create new ones. (Moving back to 5.6.47 had the same issue). Note that the themes/survey-Fodler o the Server seems fine, containing four folders (vanilla, bootswatch, fruity and fruity_23.

After a (manual) update from 5.6.8 to 3.6.7

Just to understand that correctly: you downgraded from 5.6.7 to 3.6.7?

However, looking at your screenshot, you actually upgraded to 6.3.7. I small but significant difference.

What are the permissions for these folders?

Mea culpa, that typo was indeed supposed to read 6.3.7. Permissions are rwxr-xr-x, owner is www-data. Everything else (e.g. adding/editing Users and Permissions) works just fine.
Many thanks for your time

there's more content in the folder, but there is also an index file:

 

You are on PGSQL ?

If yes : hope you have a backup of your SQL data befor update

yes to both
my current workaround was to install everything anew and import relevant surveys from the lss/lsa files. that seems to work (fingers crossed), but still, it would be nice to know what happened

github.com/LimeSurvey/LimeSurvey/pull/3642
bugs.limesurvey.org/view.php?id=19262

So the only way to correct this is to recover from backups? Is there no wait to rebuild the table from the existing template folder?