docs(monitors): document public folder management APIs

[UlricQin]

Document all six public monitor folder operations. Add bilingual contracts and navigation for health, create, update, move, and delete; remove the old statement that folder writes are JWT-only.

Describe update replacement semantics, moving to the root with explicit dest_parent_id: 0, and 409 FolderNotEmpty when child folders, alert rules, or dashboards block deletion. Keep product-specific and consolidated specifications in sync.

Validation:

• python3 scripts/lint_openapi.py passed across all 12 spec files.
• python3 scripts/api_path_redirects.py --check passed.
• Mintlify build and broken-link checks were not run because the Mintlify CLI is not installed locally.

Publish alongside the fc-pgy change that enables App Key authentication for the five newly documented endpoints.

Related PRs:

• Gateway: https://github.com/flashcatcloud/fc-pgy/pull/1273
• SDK: feat(monitors): add public folder management APIs go-flashduty#102
• CLI: feat(monitors): add folder management commands flashduty-cli#232
• API documentation: docs(monitors): document public folder management APIs #1058