Switch picture on TV but have the same picture streaming over the laptop. Is that possible without a cell phone that films?

I have my own Twitch account and would like to stream games from my Switch on this channel. However, my laptop can't stand streaming and playing games at the same time. I've already tried a capture card, but then I only see a very small jerky picture. This is very bad in such fast games like "Rocket League" because these stuttering can usually cost you a win. I would appreciate your answers, thank you

Yes with a capture card

I tried it with one but always got the jerky little picture in OBS Studio and the picture was only on the laptop and not on the television

Maybe the laptop is not suitable for streaming? Too weak?

Probably