Extract video from sniffing Network Traffic

Hello!

I know that it is possible when I am watching for example a youtube video to sniff my own Internet Traffic with WireShark and extract the video file I am watching from it.

I don't know how WireShark saves that video file but something like .mp4, .mpeg, …

I want also to extract a video from my sniffed data packages but I don't want to have a video file, I want do have a streamable file which I can stream to another source.

For Example:

I am watching a Live Stream on the Internet, so I will sniff all my traffic, extract the live stream from my data packages and instantly stream that live stream to some other source.

My Question is: Is that possible and if so, what steps/programs/ideas would you recommend to get a solution on that problem?

Maybe forget WireShark and write an own program? If so: Which language?

Thanks in advance and have a greate Day/Night!

I want also to extract a video from my sniffed data packages but I don't want to have a video file, I want do have a streambl .file To make a locally stored video into a remote stream you would need to host the file yourself. Is that possible and if so, what steps/programs/ideas would you recommend You could use a screen recorder or video capture prog on the original stream and then just re-broadcast it,  or get the HTML code and embed it in a webpage then link to that.

Thanks for your answer. Screen Capturing is no option for me because I want to restream it on my Server which doesn't have a GPU. I found a .m38u file and I could use that file to stream it on VLC Player so the next step will be to restream it.

iframe, rtmp, rasp pi, site, rest should be straight forward