Unfortunately WP Embed isn’t responsible for converting links into iframes.
The conversion of links and shortcodes into iframes is implemented by OEmbed and that happens via OEmbed APIs on the_content filter in PHP, not javascript.
It’s much more likely that your transitioning to pages that use raw post content rather than processed/rendered content, e.g. templates that incorrectly use echo get_the_content(); or echo $post->post_content; to display their data, or use the raw content from the REST API. This is because those methods don’t pass the content through the_content filter which converts links to OEmbeds, processes shortcodes, and renders server rendered blocks etc
WP Embed deals with iframes that already exist and helps with handling embed height. It already has DOM event listeners for when new DOMContent is loaded.
Triggering WP Embed is not your problem or the solution you are looking for, and your problem has nothing to do with WP Embed. You will need to look elsewhere to diagnose what is happening.