I think you want the following ggplot code. The geom_bar() will count how many times each value of button appears, subdivided by values of relevanz.
ggplot(buttons_long,aes(x = button)) +
geom_bar(aes(fill = Relevanz),position = "dodge") +
scale_y_log10()
In your original code
ggplot(buttons_long,aes(x = button,y = wert)) +
geom_bar(aes(fill = Relevanz),position = "dodge",stat = "identity") +
scale_y_log10()
you set stat to identity. The geom_bar() then plotted the value of wert for each level of Relevanz. Since wert and Relevanz are the same information expressed in different forms (gar_nicht_wichtig = 1, Nicht_wichtig = 2, etc.), your plot was identical for every level of button.