[Feature]: Add support for stored search templates

### Problem Statement

Our team is migrating to centralized, stored search templates to manage all search requests across multiple clients. Currently, Relevance Studio does not support the ingestion or utilization of these centralized templates. This forces us to manually replicate and maintain identical search queries in multiple places, creating a high maintenance burden, increasing the risk of configuration drift, and defeating the purpose of a centralized architecture.

### Proposed Solution

We would like Relevance Studio to natively support stored search templates. Specifically, the platform should be able to:

1. Fetch/Reference a centralized stored template.
2. Accept dynamic parameters at runtime to pass into the template.
3. Render and test the relevance of the query based on those parameterized inputs.

### Alternatives Considered

We considered continuing to manually sync queries between our codebase and Relevance Studio, but this approach is error-prone, non-scalable, and creates unnecessary overhead for our engineering and product teams.

### Enhancement Area

Frontend (UI)

### Priority

Medium - Nice to have

### Use Case

_No response_

### Additional Context

_No response_

The issue identifies the Frontend (UI) as the enhancement area but names no files or tests. Start by locating the UI entry point for search requests and relevance testing, then trace how request inputs are represented. Done means the UI can reference a stored search template, accept runtime parameters, and render and test the resulting query.

Written by the indexing model from the issue text.