OK, I went a bit further.
When I comment out the line, the module works. The button "Install available languages" is not doing anything (what I can understand, as this line assigns the NavigateUrl). I added a label to the module ("TestLabel") and added the line
TestLabel.Text = (var == null ? "NULL" : var.FullUrl)
right under the out-commented line. This displayed "NULL".
I then searched the Tabs table for a record with TabName = 'Extensions' - this one I found (as a child page of "Host". I also found a tab with the name "Erweiterungen" - the German translation for "Extensions" as a child page of "Admin". When I change the code in the line above the line that fires the extension to
var tab = TabController.Instance.GetTabByName("Erweiterungen", Null.NullInteger);
the whole thing works.
I changed back the code, and renamed the tab "Erweiterungen" to "Extensions" - voilà.
This leaves some question marks in my head. My conclusion is that someone must have (accidentally?) deleted the original Extensions page from the Admin menu and then created a new page called "Erweiterungen" and placed the Extensions module on that page.
But finally, it works.
Happy DNNing!
Michael