You are incorrect about mammograms. While men can get breast cancer, mammograms are generally not recommended for them because of the relatively low occurrence rate and that fact that they are designed for larger breast tissue mass. However, that may not apply to the transitioned population (both directions). It depends on a number of factors and should be discussed with a medical professional.

Some sauce for those that are curious:

https://transcare.ucsf.edu/guidelines/breast-cancer-women