Add project finder for eligible projects

What does this MR do and why?

With ad-hoc indexing of Code Embeddings, we can't rely on the Projects GraphQL query's withCodeEmbeddingsIndexed filter (introduced in !195699 (merged)) to populate the projects in the /include <repository> command. Instead, we should populate the /include <repository> with projects that are eligible for Code Embeddings.

This MR introduces a withDuoEligible filter on the Projects GraphQL query that filters on projects that:

  • have root namespaces with AI-supported plans
  • have Duo features enabled

References

Related to #576635 (closed)

feature flag: #578113

Screenshots or screen recordings

Before After

How to set up and validate locally

Screenshot_2025-10-21_at_20.16.18

SQL and query plan: !209581 (comment 2844092880)

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Edited by Pam Artiaga

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