It would for streaming art on my NSFW account and games on my SFW account.
The art might be fine, might be worth doing a test stream just to see how the laptop performs while streaming and making art at the same time. If it's running Windows 8 and struggles with Legacy of The Duelist, I wouldn't even bother trying to stream while playing a game.
I really need a new computer because I will be unable to use my current laptop in 2024 because nearly every program I use will stop supporting Windows 8 in 2024.
When they say they'll stop supporting windows 8, it's likely referring to compatibility with future updates, so you should be able to just avoid updating them and it should work fine. However, if the program uses cloud features or often makes queries to a server (Like Adobe's Creative Cloud suite) that may not be the case. I recommend looking at what the end of support messages for each program says.
I don't know how to update Windows, or if it costs anything to perform such an update. And, even if I figure out a way to update this laptop, I have no idea on how to upgrade the inner workings of it to make it suitable for streaming and playing games.
Unlike desktop computers, almost every laptop is designed such that it is not upgradeable by the end user and seeing as yours is running Windows 8, that is almost certainly the case. You basically have no choice but to buy a new one.
Coming from Windows 8, you're supposed to buy a new license, but I wouldn't. There are ways of pirating Windows.
I would give suggestions on what to get, but seeing as I live in Australia, I can't really provide good information for the American retail market.