I wouldn't wait, these updates can take months or longer to happen, if anything I would say you're late. If you don't want the male gender marker anywhere, then do everything you can to start removing it.

Also, I wouldn't worry about leaving or entering the country based on gender marker alone - make sure you have extra copies of your court ordered name change (my court listed gender change as the reason), and this will usually be enough whenever questions start to arise - it unilaterally proves you were your deadname.

Also, it's possible that if the ship rights itself politically, that in a matter of a few years you will be allowed to self-identify gender markers again.

EDIT:

here are the places I updated name and/or gender:

• social security
• passport
• birth certificate
• driver's license (Real ID)
• voter registration
• marriage license
• email address
• bank & other financial institutions (credit card company, etc.)
• employer
• on school transcripts (high school, college, etc.)
• credit bureaus: Equifax, etc.
• your house's utility company
• any property deeds, e.g. to a home or car
• medical doctor
• eye doctor
• insurance companies (medical, auto, etc.)

I would move fast on getting name and gender updated on a Real ID driver's license, the federal government is already moving to try to deny trans identity for Real ID, so you want to get on that - it will allow you to fly anywhere in the U.S. without requiring a passport that may not have your correct gender marker. Getting a Real ID license with your updated name and gender marker would then allow you to update your name lots of other places, it will be accepted as a legal ID.

Currently I think social security and passports cannot have gender marker updated, but it's still worth updating the name, and on the passport it can be important to have an accurate photo.