By and large, anxiety is exacerbated by poor class fit, and reduced by good class fit. So most gifted kids tend to be much happier in a GT class where the material is taught at an appropriate level and speed, and they are with peers who are more likely to share interests and "get them".
That said, "good fit" is a complex thing, and especially tricky when you're dealing with 2E. DS, for example, went into serious depression in grade 3 from mass quantities of repetitive busy work. The next year, in contrast, anxiety went through the roof because he couldn't cope with serious high-volume writing expectations of a more advanced class. DD hit clinical levels of anxiety when undiagnosed dyslexia made keeping up in an advanced grade 2 class harder and harder for her. She's now remediating, happy and low-anxiety - but frustration with "boring" regular-level grade 3 materials is taking over. It's devastating, I know, to see your child crushed under the weight of their own worries.
Many people on this board have described GT classes that are more geared to high-acheivers, and tend to high volumes of work rather than more complex/ accelerated work. While the latter can be a sigh of relief for many gifties, the former can be misery to some, especially if executive function, writing, or other issues are also present.
The right fit can require a difficult combination of simultaneous challenge and accommodation, and is utterly unique to each child. The more you can observe the classrooms and talk to the teachers, the better it will help you figure out where your DD will be best supported and challenged. Hopefully, your GT class can provide the kind of environment you are looking for.