Did you get anywhere with this? I’ve just written a plugin that does exactly this job. It’s basically a cron job that scans all your posts & pages to create an internal index of which images are where. It then synchronises your Media Library alt text with the images in your content. It’s based on the code from this tutorial: https://wp-tutorials.tech/refine-wordpress/filter-for-images-missing-alt-text/ but the plugin builds on it to add the synchronisation stuff. There’s al link to the plugin from the tutorial page.
But… it all comes down to page-builder integration. The plugin currently only has Gutenberg and Classic-Edit integration at the moment. I need to add Elementor/Divi/etc integrations… a bit of a pain, but it has to be done.