The ruling does not determine the definition of ‘woman’ in all situations/ circumstances, but it does determine what it means in law when it comes to unequal treatment of males and females. So schools could promote the ‘transwomen are women’ narrative still. If teaching about or citing the law, they would need to say that the term ‘woman’ when used in uk legislation refers to females/biological women.
The EA requires people with protected characteristics to be treated equally to those without these characteristics unless there is a legitimate aim for not doing so, and the ‘unequal treatment’ is proportionate to achieving the aim.
In England, schools are required, by law, to provide single sex changing rooms and loos. The legitimate/proportionate reasoning has been applied by government. The ruling has clarified that access must be determined by sex. Schools can provide gender neutral facilities, but these must be in addition to single sex ones.
If/where schools wish to treat pupils differently / segregate them in line with any protected characteristic or combination of characteristics (e.g race, disability, sex, gender reassignment), they need to have a clear and justifiable rationale for doing so. It is highly unlikely that they can use ‘force teaming’ to group children with the protected characteristic of female with males with the protected characteristic of gender reassignment (and vice versa for males). I don’t think there is any circumstance/ situation where this could be viewed legitimate and proportionate.