Masha may not be around still to read this, but I'd like to point out that there is a practical reason for using phrases like 'trans IDing man' or 'transIDing woman' - it's obvious that people are not at all clear what 'transwoman/ trans woman' or transman/ trans man' actually mean.
It's apparent that some people focus on the element 'woman' and so think that a trans woman is a biological female who IDs as/presents as a man... because they are a 'trans' woman.
There's a certain logic to that, isn't there?
So why not let trans women use the women's toilets? after all, they are biological females who present as 'trans', right?
And trans men need to be aware of issues like prostate cancer because they are men, right? Men who are 'trans', so although they present as women, maybe have had hormone treatment and surgery, it's important that trans men are included in men's health messaging...
You see the pickle people can get into with the terms 'trans woman' and 'trans man', Masha?
The use of 'trans-identifying' followed by the biological sex of the person is much clearer: it asserts their transgender ID, but clarifies the sex they were born into, and which they will always retain, no matter how much hormones they take or surgery they have.
It's not only less confusing linguistically, but it also simplifies the operation of EA2010, which, as the UKSC confirmed [note: confirmed the existing law, it didn't change the law]operates on the basis of biological sex.
A small number of facilities are separated on the basis of sex - not gender, gender ID, transgender ID or anything else, just sex as in biological sex.
It's much easier to understand which facilities transwomen should use if they are referred to as 'trans identifying men', so there is no confusion about which EA2010 category they belong to - they are, in the first place, men, however they identify, and therefore should use facilities designated for men.
The terms 'transwomen' and 'transmen' will continue to be used as a kind of shorthand, but when it is necessary to be clear and accurate e.g. in the application of the law, health and safety protocols, workplace regulations etc etc, they are misleading and unhelpful.