No, section 7 is about ‘gender reassignment’
‘A person has the protected characteristic of gender assignment if the person is proposing to undergo, is undergoing or has undergone a process (or part of a process) for the purpose of reassigning the person’s sex by changing physiological or other attributes of sex’
One might question what said attributes of sex are and how this could be reassigned but this is not quantified/qualified in any way as far as I can see. Indeed, the SC judgement para 89 and 90 explicitly noted that this is evidenced by documents for the purposes of a GRC, and there is no guidance on what are male/female names and what it means to live in an acquired gender beyond the person’s name.
The SC judgement mentions ‘gender identity’ once, in paragraph 203 to make the point that they could see no reason why the legislature would have intended that people with the protected characteristic of gender reassignment should be treated differently depending on whether they have a (confidential) certificate, ‘even though in many (if not most) cases there will be no material distinction in their personal characteristics, either as regards gender identity or appearance …’
The GRA 2004 uses the term ‘acquired gender’ in the context of gender dysphoria. One would have to go back to the drafting stage of this to see if the phrase ‘gender identity’ was used (if I recall correctly, the term predates 2004), but these documents won’t be released until early 2030s depending when they date from (because of the thirty year rule on govt papers), but the legislation does not use it nor does the SC judgement.