Is the Prophet (peace be upon him) authentically reported to have said: "There is no prayer for one who is held back (or constipated)" and who is "the one who is held back (or constipated)"?

There is no hadith with this exact wording. Rather, what is authentically reported is the hadith from Abu Umamah in Ahmad and Ibn Majah: "Let none of you come to prayer while holding back urine" and "He ﷺ forbade a man from praying while holding back urine." Its chain of transmission is sound. Al-Haqin is one who is holding back urine.