What is the ruling on prayer after the discharge of dark-colored vaginal secretions following the cessation of birth control pills and before the onset of menstrual bleeding?

These dark discharges are "al-Kudrah" (brownish discharge). According to the Hanbali school of thought, they are considered menses if they occur during the usual period of menstruation, but not if they occur outside of it. This is based on the statement of Umm 'Atiyyah (may Allah be pleased with her): "We did not consider yellowish or brownish discharges after purification to be anything." Accordingly, you should not stop praying unless you see menstrual blood, unless these discharges occur during your usual period.