I managed to update to Version 6 as follows (don't know, if Step 1 and 2 are really helpful):
Started up Windows 10 and updated to Version 6 of Enpass
Turned on Synchronization with my Google Drive account.This seemed to convert my Data to Version 6 compatible database.
Now rebooted to Linux and completely removed Enpass
Installed the Enpass Extension in Chromium Browser
Re-Installed Enpass Version 6 for Linux
Started Enpass as a "New User"
Enter Master Password
Enabled Sync. Now the credentials for my Google Drive account could be entered, since the browser opened now.
Hope this helps.
It is important, that the Browser-Extension is compatible with the installed Desktop-Version, otherwise, the Browser is not launched to enter the credentials for the Sync (e.g. Google Drive).