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"Struggling to understand the teacher's explanation (or understanding it well in a second language) is not a substitute for an accelerated and enriched STEM programme."
On the other hand, in the USA opportunities for native English speakers to learn a world language as children are rare. Families interested in supporting their children's interest to be bilingual/multilingual may find immersion programs to be their only option.

Some may say it is precisely the "struggle" that gifted children crave and thrive on, as it may provide a suitable intellectual "challenge" for them while they are learning to puzzle together the language. Once the language is mastered, they would benefit from appropriate curriculum and pacing.

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the likelihood that even if she's really bright, she will be able to benefit from enrichment at home regardless of whether she's in immersion, regular classrooms, or a gifted program.
Yes, all kids may benefit from enrichment at home: support from parents to learn and explore in the child's area(s) of interest.

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At most it will be more work for me.
Spoken with the freshness and anticipation of a parent at the beginning of the journey. laugh Yes, it can become rather bedraggling to keep up with a gifted kiddo. crazy

I believe your planning and careful consideration of the options will be very beneficial.