Welcome!
Of course the scores could have been affected by attention, anxiety, having a cold, or being a young child (though usually scores are reasonably stable by this age). Or any number of other things. I will say that the first 30 minutes of an average WISC covers many other areas besides verbal comp (the first half of the test includes subtests from each of the five primary indices), so I wouldn't overinterpret the impact of settling into the test on any one index. Also, effusiveness is not necessary for scoring well. Typically, I see the most effects from anxiety and attention on the WMI and PSI tasks, and sometimes on other timed tasks, such as the VSI subtests.
On the question of whether you are deluding yourself in identifying her as GT: well, your evaluator, who not only had the scores you've posted, but also her clinical observations and other assessment data (history, etc.), appears to identify her as such, based on the resources and directions you've been given by her! And GT doesn't mean everything necessarily comes easily, as I'm sure you know. So ID'ing giftedness is more likely to be helpful than harmful, but obviously isn't in isolation; she has strengths, and she has challenges (as we all do), and being clear-eyed about both is very far from being deluded.
It sounds like some areas to ponder might include finding an understanding peer social group (perhaps the GT cluster will help with that), addressing the anxiety (probably ahead of the attention), and perhaps doing a little social-emotional learning/social skills training, mainly to get a little fluency with social-emotional problem-solving. I mention that last item because my observation is that, for many young people with relative weaknesses in processing speed versus reasoning ability, their social challenges are related to the increasing pace at which social communication occurs as NT children increase in social sophistication. Have an untimed conversation, and many of them can problem-solve quite adequately; they struggle to absorb, analyze, and apply these skills in real time. Overlearning can help, as can learning subtle strategies to slow down other people's social interactions (aka, stall), such as reflecting/reframing and placeholder phrases.
