You ask great questions. While parents with gifted kids would tend to be inclined to seek schools in which their children would have true intellectual peers, what is seen on the surface may not be the same as what lies beneath the veneer.
My first thought would be to look at the school district's website and see what you can find about "gifted." For example, the district may tout activities or acceleration for gifted students, run a group for parents of gifted students, and/or have policy related to identifying gifted students and/or meeting the needs of gifted students. Look for chess club, robotics club, and other activities which could be created in your school district.
My second thought would be that while "desirable" districts may drive up housing costs, correlation does not mean causation.
Consider two neighborhoods: one community may have building/zoning requirements for larger lot sizes, homes with particular square footage requirements, and certain percentage of brick or stone. This community may have stringent municipal code enforcement for permits, lawn care and landscaping requirements, and regular property inspections. This community may therefore attract people who can afford the constant cost of upkeep at a fastidious level and lead to the turnover of homes purchased by those who cannot keep up at the mandated level. Any higher property tax generated in this neighborhood may be used by the local government (municipality and/or school district) to create favorable branding/marketing campaigns, forge bonds with local realtors (competition for housing leads to bidding wars and raises prices), manage the press and influence social media. The amount which each family contributes to fundraisers may be tracked, and favoritism shown to high-dollar-donors in the form of additional opportunities and awards/accolades for their students. A carefully contrived and controlled narrative, funded by taxpayer dollars.
An interesting exercise is to practice stating any simple occurrence in both positive/favorable and negative/disfavorable terms, by use of different tense, adjectives, perspectives, and selectively including or omitting details. Strive for opposing narratives which are both true, but emphasize different elements. This exercise may be seen as being related to lists of gifted characteristics, portrayed in both positive and negative light. One example of such a list -
https://gifted-studies.com/ptp/wp-c...ren-Positive-and-Negative-Behaviors-.pdf