Simply states that the House and Senate may punish their members. Does NOT state that the judiciary cannot.
This clause PREEMPTS the Executive and Judiciary. Now, concerning Commander in Chief, maybe not, particularly if the member is a rebel or something. Presumably even a militia member could shoot one.
Lots and lots of these more obscure Constitutional clauses were exercised (and with that much better understood) as the Confederates left the Congress way back when.
Good to read about what Congress did then.
The Congress is authorized to "punish members". It is un-necessary to further elaborate on that.
Now, get back to that ground glass, and don't grind it too fine. We want some real blood here.