You are close to understanding, but I think the "trans" issue is clouding your line of thinking.
I believe it is promoted by the populist media and politicians as a shift away from community and towards the individual.
Agree.
A good example is how the trans debate has taken over everything else for some mumsnetters.
No, this is a very bad example. The concern of many women on MN is to protect their rights as females, not to signal their identity or individuality as women.
Identity politics began as a tool for liberation but has been taken over by the elite.
Specifically, the elite left - so they can be "the good people" and virtue-signal about protecting minorities whilst still keeping taxes low.
It now often emphasises individual recognition over collective struggle
Usually the opposite: those who claim a special "identity" like to join a collective struggle for rights and recognition (a very valid thing to do if they have been denied rights historically).
The collective struggle that has been abandoned is class-based justice for workers and the poor.
for example, mumsetters who would choose a right wing representative as the party ‘protects women’ despite the party not protecting the poorest, when its women who suffer the most in poverty.
As above, this is a poor example. Your thinking is muddled. It is necessary to be able to define what a woman is before looking at how many women are in poverty, so the priority has to be protecting the legal status "woman".
Capitalism benefits by commodifying identity and turning it into a personal brand.
Agree.
This shift towards the focus of the individual fragments solidarity and weakens movements aimed at systemic change.
Agree. But as I said above, many people who have an "identity" do so for political purposes, to increase solidarity and effect systemic change.
e.g. identifying as disabled.