Consider using template enhancement output buffer introduced in WordPress 6.9

[chesio]

See: https://make.wordpress.org/core/2025/11/18/wordpress-6-9-frontend-performance-field-guide/#introduce-the-template-enhancement-output-buffer

[chesio]

Putting the implementation on hold for now as it only supports HTML content type, so we would either need to drop support for caching of XML sitemap or keep the old code anyway.