Greasy Fork

Those embedded iframes https://www.instagram.com/reel/XXXXXX/embed/ cannot be played inside the embedded frame.

Is there a userscript that allows embedded Instagram videos to play instead of open a new tab to browse instagram.com?

I don't use Instagram. But maybe a solution like this will suit you

If that doesn't help, try modifying Sec-Fetch in the Headers request

In general, it is best to compare the video that opens in embed with the one that is forbidden. To identify what is blocking playback.

If the video is blocked on the Instagram side. But the only way is to pass access tokens into the request (this is unsafe). Perhaps there are mirrors. Then you can try through them (with modified Content Security Policy (CSP))