@suggestionsplease1 There are several reasons why it is not helpful to look at what has happened in other countries which have brought in self ID.
One reason, as various people have noted, is that there is no guarantee that any relevant data is being collected. Indeed, I doubt any government would want to collect data which might show its decision to introduce self ID to be a catastrophic one.
Another reason is that all countries are different and the impact of self ID depends largely on what transgender people were allowed to do before self ID and what they were allowed to do after self ID.
The UK does not have self ID, and yet, up until the Supreme Court judgment it was accepted by most people that trans people could use single sex spaces for the opposite sex. My understanding of the Equality Act was that they could be excluded from single sex spaces for the opposite sex, but that it was essentially discretionary, and up to the organisers of that space to decide. The Supreme Court judgment came as a surprise to me, albeit a very welcome one.
In countries where trans people were already using single sex spaces for the opposite sex prior to self ID, or where single sex spaces are uncommon, I would not expect to see any measurable detriment to women and girls following the introduction of self ID, because the harm to them would already have been baked in.
Hypothetically, in countries where trans people are banned from using single sex spaces for the opposite sex unless they have changed their legal sex, I would expect the introduction of self ID to have a measurable impact. But I am not aware of any such countries.
In these countries, access to single sex spaces in public places is granted on the basis of trust. Self ID or no self ID, nobody is checking IDs on toilet doors so it is largely irrelevant. Where self ID may have a real impact is in the limited scenarios where access to a single sex space is gatekept by someone in a position of authority, such as prisons or hospitals. And we have seen a high number of bad outcomes in both those environments, both in the UK and in countries with self ID such as Ireland (the home of the fragrant "Barbie Kardashian").
In the UK, we could bring in self ID tomorrow, and, providing the Equality Act was not amended to make "sex" mean certificated sex, it would not change a great deal for trans people, who would still not be allowed to use single sex spaces for the opposite sex.
So when you talk about self ID, I am not sure whether this is really what you mean. Are you really talking about the ability to change your legal sex on a declarative basis? Because in the UK changing your legal sex now has very limited impact post Supreme Court judgment.
Or are you talking about trans people being able to self identify as members of the opposite sex for the purposes of using single sex spaces for the opposite sex? Because that is not self ID, and it happens in many countries, even those without self ID, and including the UK until the Supreme Court handed down its judgment in April.
So it would be helpful to know what you are actually talking about when you refer to countries which have implemented self ID.