Add application_json.log to docs

What does this MR do?

This MR adds documentation for application_json.log that was recently introduced in !22341 (merged)

Related issues

#22812 (closed)

Author's checklist

• Follow the Documentation Guidelines and Style Guide.
• [-] If applicable, update the permissions table.
• [-] Link docs to and from the higher-level index page, plus other related docs where helpful.
• Apply the documentation label.

Review checklist

All reviewers can help ensure accuracy, clarity, completeness, and adherence to the Documentation Guidelines and Style Guide.

1. Primary Reviewer

• [-] Review by a code reviewer or other selected colleague to confirm accuracy, clarity, and completeness. This can be skipped for minor fixes without substantive content changes.

2. Technical Writer

• [-] Optional: Technical writer review. If not requested for this MR, must be scheduled post-merge. To request for this MR, assign the writer listed for the applicable DevOps stage.

3. Maintainer

1. Review by assigned maintainer, who can always request/require the above reviews. Maintainer's review can occur before or after a technical writer review.
2. Ensure a release milestone is set.
3. If there has not been a technical writer review, create an issue for one using the Doc Review template.