Add group query builder and refactoring

What does this MR do and why?

Summary

This change adds Elasticsearch-powered search for GitLab groups, making group searches faster and more relevant. When the feature is enabled, searching for groups will use Elasticsearch, with support for filtering by visibility (public/internal/private), parent group, organization, and archived status, as well as flexible sorting options.

We will add support for basic search (using postgresql) later on in future MRs.

References

Screenshots or screen recordings

Scope	Advanced	Basic
Group
Global

How to set up and validate locally

Run the following in the rails console:

Feature.enable(:elasticsearch_group_search)
client = Group.__elasticsearch__.client
index_name = Search::Elastic::References::Group.index
groups = Group.limit(10)
Elastic::ProcessInitialBookkeepingService.track!(*groups)
Elastic::ProcessBookkeepingService.new.execute
Elastic::ProcessInitialBookkeepingService.new.execute
user = User.first
query = Search::Elastic::GroupQueryBuilder.new(
  query: 'gitlab',
  options: { current_user: user }
).build
response = client.search(index: index_name, body: query)
puts "Results: #{response.dig('hits', 'hits').size}"
response.dig('hits', 'hits').each do |hit|
  puts "  - #{hit['_source']['name']} (ID: #{hit['_source']['id']})"
end

Or we can test it via handlers

search_results = Struct.new(:current_user, :query, :filters).new(
    user,
    'gitlab',
    { order_by: 'updated_at', sort: 'desc', page: 1, per_page: 20 }
  )

  handler = Search::Handlers::Groups.new(search_results)
  results = handler.send(:fetch_results)

  puts "Results: #{results.size}"
  results.each do |group|
    puts "  - #{group.name} (ID: #{group.id})"
  end

MR acceptance checklist

Evaluate this MR against the MR acceptance checklist. It helps you analyze changes to reduce risks in quality, performance, reliability, security, and maintainability.

Related to #607018 (closed)