I am checking this area with EO Browser (I would strongly recommend you use EO Browser instead of Sentinel Playground for such tasks, as it allows you to do much more accurate analysis), I see many dates in June, i.e.
and many more, almost every second day.
What do you mean that you can’t see these dates using WMS?
I notice that your WMS configuration has cloud coverage filter set to 20%. Try setting this to 100%, so that you see all available data: