Questions about Xbox 360 Storage device/data transfer

I’ve had my Xbox 360 for quite a few years now (my brother first bought it sometime in I think either 2016 or 2017). In all the years we’ve owned it we’ve never had anything wrong with it. the thought of something going wrong with it has never crossed my mind, not until recently. I saw someone else make a post, showing that there was a weird visual effect on their screen from their Xbox 360, and the comments said they’d have to eventually get a new Xbox (i believe it was from their gpu or something).

That made me think about my own Xbox 360. While there isn’t anything wrong with mine at the moment, I was wondering in the event that it were to shut down, would there be any way to transfer the data to another Xbox 360/xbox one? Would simply putting its storage device on another Xbox 360 work, and all our profiles/game data still be there? I’m not the greatest with technology and just want to be prepared in case something happens.