💡 Integrate SyncAI Natural Language DRep Search in DRep Directory

### Area

Delegation Pillar

### Is there new design needed?

Yes

### What?

Introduce a **natural language search feature** in the **DRep Directory**, powered by **SyncAI**.
This feature will allow users to search for DReps using **conversational language** (e.g., "Find me all DReps with more than 100 million ADA delegated to them") using the `/drep-ai-search` API endpoint provided by SyncAI.

API reference: [https://docs.syncgovhub.com/api-reference/drep-api](https://docs.syncgovhub.com/api-reference/drep-api)

The integration should work as an **alternative** to the current keyword-based search, giving users more flexibility in how they explore and assess DReps.

### Why?

- Improves **user experience** by enabling intuitive, human-friendly searches.
- Makes it easier for users to **discover DReps** based on specific, complex criteria without needing technical knowledge.
- Supports the goal of **more informed delegation decisions** by simplifying access to filtered DRep data.
- SyncAI’s response includes **metadata explaining the filtering logic**, increasing transparency and trust in results.

### How?

- Add a **“Search with SyncAI” button** (with SyncAI logo) next to the current DRep Directory search bar.
- When clicked, open a search field or modal that accepts **natural language queries**.
- Send user input to the `/drep-ai-search` endpoint and display the filtered results.
- Include a “Powered by SyncAI” label and logo alongside the returned results.
- Display a summary of the **filtering logic metadata** returned by SyncAI to explain how results were selected.
- Maintain the existing keyword search as a parallel option.

### (Optional) User Story with acceptance criteria

- [ ] A **“Search with SyncAI”** button is added to the DRep Directory UI.
- [ ] Users can input **natural language queries** that are sent to the `/drep-ai-search` API endpoint.
- [ ] Results are displayed using the same UI layout as existing DRep listings.
- [ ] Each result set includes a **“Powered by SyncAI”** label and logo.
- [ ] Existing search functionality remains unchanged and usable in parallel.