Streaming doesn't require much in terms of specs. You could stream with a Mac mini or MacBook Air 13" or Pro 13" and save a lot of money.
That being said if you are going to spend the money I think a slightly better than base model would do. M1 Pro 16 core GPU and 16 gb ram should do just fine.
Also your 2014 Mac is a completely different animal than the M1 Pro/Max or any M1 for that matter. You will see huge performance difference on M1!
If you are streaming and screen is important-one reason to get the new MBP is the screen for sure. So I would suggest getting the 16" model as the extra screen makes a huge difference. It really depends on how you use your Mac.