YouTube video player on Product in Woocommerce

I manage an e-commerce site in WooCommerce based on the ‘Modern’ theme. Currently, in the product gallery, I can only display .mp4 files natively, while YouTube and Vimeo links open in an annoying pop-up.

I need a solution that:
• integrates YouTube and Vimeo videos and Shorts (and, while we're at it, other external players as well) directly into the same gallery cell, just like .mp4 files;
• eliminates all pop-ups;
• maintains video quality without compromising site performance;
• does not conflict with the theme or the rest of the configuration.

I prefer a clean solution in a child theme or using targeted snippets, documented and easily restorable. When finished, I would like to test a couple of sample products together to confirm that everything works on desktop and mobile.

Product link:
https://shorturl.at/YvsAh