Firstly, the overwhelming consensus of medical research indicates that menstrual synchronisation doesn't exist.
Secondly, if you are cycling progesterone, your hormone levels will naturally fluctuate in a cycle approximately similar to cis women. Your experience of emotion, circadian (sleep) cycles, parenting propensity, pheremones, etc will all cycle accordingly. It's possible that the hormone cycle might coincidentally align with other women.
Your stomach cramps, unpleasant as they sound, are unlikely to be related to your hormones. Period pain (menstrual cramps) in women is associated with contractions within the uterus. When the uterine muscles contract, they constrict the blood supply to the tissue of the endometrium, which, in turn, breaks down and dies. These uterine contractions continue as they squeeze the old, dead endometrial tissue through the cervix and out of the body through the vagina. These contractions, and the resulting temporary oxygen deprivation to nearby tissues, are responsible for the pain or "cramps" experienced during menstruation.
Emotional systems in menstruating women are often the result of hormone changes in the luteal phase. If your hormones are changing during this time - eg, because you forgot your medications or you just received a new implant or injection - then that might have similar emotional effects for you. Symptoms are things such as moodiness, depression, anxiety, crying spells, irritability, etc.