How can I create custom shareable embed links for media like Spotify or SoundCloud?

Some websites and applications, such as Spotify and SoundCloud, generate unique embed links when sharing a song or video. These embeds are more than just static content; they allow users to play the media directly.

For example, here’s an image of Spotify’s embed:

I attempted to create a basic embed using the tag, but I want something more functional and dynamic, like the ability to play the track or video directly from the embed. Does anyone have suggestions for implementing this with custom functionality (e.g., custom player controls)?

Any help or libraries to explore would be appreciated!