Look at every single plan during open enrollment. Call the insurance companies directly (not the benefits center, trust me I used to work for Aon Hewitt and it's a joke) if you have questions. They can also help you find a doctor. See if the procedures can be paid for with a health savings account, which is a tax-free contribution from your paychecks to pay for medical expenses (they are a lifesaver).
I'm not in your situation but I congratulate you and wish you the best <3

Edit: from what I understand, open enrollment is August 6-24.

They’ve been covering them for years! That’s how I had mine. Wait for open enrollment & pick your plan (make sure the plan covers HRT if you need it to, specifically what you’d be taking- they have a site you can plug in the drug name to check the copay). The fee you see next to each plan comes out of your paycheck every week, and be sure to check that deductible to make sure it’s good for you. Starbucks also has a help line you can call while you’re enrolling to help you choose a plan. All the info on that will be provided once open enrollment starts and they send out the info cards/post it on the hub. Also don’t be afraid to ask your SM and fellow baristas about how they did it, if they get their insurance through sbux! Most people won’t ask why you need it, and it’s easy enough to give a general answer if they do and you don’t want to get into it.

Open enrollment should start in August, so long as you meet the criteria for being eligible you should be able to enroll then. I would suggest posting over in r/starbucks though, it's a much more active sub so you might get responses from people in similar positions