What is the ruling on a menstruating woman performing the prayer with a congregation ostensibly (movements without recitation) to avoid embarrassment?

What you did, feigning prayer while menstruating, is an unlawful act. There is no sin in menstruation; it is something Allah has decreed for the daughters of Adam. Scholars have explicitly stated the prohibition of feigning prayer without intention. Seek Allah’s forgiveness, and do not repeat such an act.