Yes, that GAI is correct, based on the scores you've provided.
Generally speaking, GAI is a more reliable measure of giftedness, as the indices that go into it are more heavily loaded for abstract thinking and problem solving skills, and less closely associated with rote efficiency. This doesn't mean that there is no value in having a high PSI; actually, having MG reasoning in combination with MG PSI may be more functional for most people than having HG reasoning and, say, Average or below PSI.
VCI is notably higher than PRI, which does suggest that she may have a verbal preference. In a much lower-functioning child, this difference might present as learning challenges, possibly in mathematics or writing, but where she has no index scores below the Superior range, there is no obvious reason to believe that this would be the case for her (unless you have other data that suggests there is).
Her early experiences viz diverse cultural and linguistic experiences are unlikely to have any relationship to her high PSI. They are more likely to have affected her VCI. Given the speed with which she appears to have picked up English, her youth when she entered an immersive English environment, and the number of years she has since spent in and English-speaking society, I doubt that she has any lingering second-language effects of the deleterious sort. There is research on fully bilingual (oral expressive and receptive) individuals that finds that their metalinguistic skills are superior to cognitively-matched monolingual learners, and that they tend to have better-developed executive functions (due to having to suppress the other language when processing one language, and from constant code-switching).
I do not recommend shopping IQ scores by searching for additional instruments, although I can see how it's a little tempting, where she misses the DYS cutoff by only 5 points. I also don't find that the SB can be accurately described as providing a more nuanced picture of a child's intellect, as a generalization. Actually, my experience has sometimes been the reverse, both in terms of nuance, and in terms of higher scores.
More importantly, this score doesn't change any of the things you already knew to be the case about her as a child and a learner. Nor is the difference between service needs for a child scoring just above the cutoff, and one scoring just below, all that significant. If she appears to be happy, growing (as an all around person, not only academically), and engaged in her current educational placement, then it may not be that critical to move on the basis of a single score. And if she is not, moving to another district may or may not resolve that.
Did the examiner give you any feedback or recommendations for instructional settings or modifications?
