Welcome JB4,
I am a retired anesthetist and spent decades working in surgery and obstetrics. I urge you to simply be an assertive consumer and let people know what you need and expect. Talk to your surgeon and team about any questions you have and let them know you are concerned about your privacy. A Procedure, Alternatives and Risks (PAR) conference is expected before you sign any permit or are sedated. I just had a surgery myself and was only misgendered once, that i know of;) My nurse at the time spoke up quickly; "Her name is Tessa!"
Mastectomy is a common procedure and does not automatically require a urine catheter but, some surgeons might prefer we have one if the procedure takes over 2 hours. A catheter, if needed, is placed in a private OR suite and your privacy should always be respected. Your fluid balance, after no breakfast or fluids all night, is monitored in part by your urine output and vital signs. Anesthetic and post operative narcotic pain medication can sometimes make it difficult to start your urine stream post op. Picture yourself awakening calmly after all is done; hungry, feeling relief and ready to go to the restroom or on a bed pan if needed. Those medications are also capable of producing degrees of amnesia and people often have no memory of even going in to the surgical room or waking up hours later. Some things are OK to forget or miss entirely
They do want you up and doing as much for yourself as possible post operatively. First you sit at the side of your bed and progress as you are able. The only people who need to see your surgical site, other than to check your external dressings, is your surgeon. Those dressings might remind you of wearing a tight binder.
If you have a trusted friend or family they can be part of your care but I hope you find your recovery team is sensitive to your needs and knows how to assist you. Your care and safety must be their first priority.
Best of luck and congratulations for getting to a better place in your life.