Fix incorrect OpenAPI examples

[dhruvkb]

Fixes

Fixes #4885 by @zackkrida

Description

This PR corrects the OpenAPI examples for

• stats, search and related endpoints (for both image and audio media types)
• removes unnecessary nesting under application/json everywhere
• removes redundant variables and arguments (code-quality improvements)

Testing Instructions

0. Check out the PR and run the API dev server.
1. Visit the OpenAPI spec at http://localhost:50280/v1/.
2. Check that the OpenAPI examples, specifically for the endpoints with corrections mentioned above, are correct.

Checklist

• My pull request has a descriptive title (not a vague title likeUpdate index.md).
• My pull request targets the default branch of the repository (main) or a parent feature branch.
• My commit messages follow best practices.
• My code follows the established code style of the repository.
• I added or updated tests for the changes I made (if applicable).
• I added or updated documentation (if applicable).
• I tried running the project locally and verified that there are no visible errors.
• I ran the DAG documentation generator (ov just catalog/generate-docs for catalog
  PRs) or the media properties generator (ov just catalog/generate-docs media-props
  for the catalog or ov just api/generate-docs for the API) where applicable.

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[krysal]

LGTM! It's nice to remove a level of indentation with the gone "application/json" in many cases.