Introduce a new Search Projects API endpoint for /include repository

Context

We added a new with_duo_eligible filter to the GraphQL Projects query, see [Code Embeddings] Add a "with eligible duo proj... (#576635 - closed).

We need to update this endpoint (or add a new one) to allow for searching by the project title and returning the most relevant results.

References

• Initial issue to update existing Project APIs: [Code Embeddings] Add a "with eligible duo proj... (#576635 - closed)
• Projects API discussion: &17298 (comment 2616391865)

Proposal

TBA