There is no test you can take that can prove you're trans or not. If there were everything would be a lot different. Instead there is a lengthy therapy requirement to get the diagnosis of gender incongruence that not even every trans person may qualify for as they may lack gender dysphoria.

What medical testing do you think would be done?

The thing is that being trans is always a self assertion, and that you fundamentally just keep asserting it long enough, and say that it is important enough that the doctor eventually agrees with you. So self-ID makes some good sense really, because it protects all trans people.

The only theoretical harm of self-id is what that a cis person might change their legal gender inappropriately? What will this do for them? If someone were a rapist it would be much easier to just walk into the changing room and rape someone. If you're going to commit a sex crime, the law that says "you have to have this legal sex to be in this room" is kind of a total non consideration you know? Like... it's like the gun free zones at American schools. Mass shooters don't really care about those laws. Because they're intending to break a much more serious law.