Because you’re on the Beta channel (and also from the database version numbers which are given in the 2.0.6.1 release notice), and because your BaseVersionName is 2.0.5.1, there’s little chance you were on anything other than 2.0.5.1 before unless you were doing exotic things like changing your update channel.
Please look for folder C:\Users\<Duplicati user account>\AppData\Local\Duplicati\updates\
Possibly you will have to tell Explorer to View hidden items (otherwise AppData may not be shown to you)
Is there a 2.0.6.1 folder there? If so, try moving it to some other directory, then retrying the 2.0.6.1 update.
About → Check for updates now (below the line that probably says it’s running 2.0.5.1) is the way to start.
Download and install as usual, and you’ll probably see 2.0.6.1 show up where the previous one had been.
The Activate button is not reliable. If Duplicati just stops, you can start it again, e.g. using the desktop icon.
When up, see what version you’re on. It should be 2.0.6.1. If it works, then next is a folder comparison for possible changes between the working 2.0.6.1 and the bad one that you moved. Easy overview is to use right-click → Properties on the folders to compare sizes and counts. Maybe some changes can be found.