Ontario birth certificate, Alberta ID ne change question

I have recently (finally) have gotten my name change application for my alberta ID, since alberta now requires a birth certificate because of their "all in one card" im now required to attain a new birth certificate from ontario before I even get my id updated because I had to surrender all my copies.

My questions are as followed:

I cannot find anything on ontario.ca speccificly about birth certificates being updated with both name and gender marker, anywhere, what paperwork do I need to fill out / is there a specific section of the site im absolutely blinded to see?

Once i have my application for name change, does it come with a completely separate section just for the birth certificate? (Reminder im in alberta, with a ontario birth certificate)

How much where the costs just to update the birth certificate name and marker? I keep seeing 137 but im assuming thats for an ontario ID too..

Obligatory fucking alberta sigh. Having the all in one card system changes is a topic for another day but this extra step is ridiculous. Don't want to get yo political in this but frick!

Any help would be greatly appreciated this process os so incredibly overwhelming :s