Issue is generally laptops have power constrained CPU & CPUs (there are certain exceptions, and engineering workstation class machines are less constrained, and a lot heavier and more expensive). For a given dollar amount, a desktop PC tends to be more powerful, as it can use more electricity and not be thermal constrained. And then you have other expansion options you lose, in exchange for lower power consumption and convenience, with smaller form factor
In general, mimicing what others have said (I've not directly compared), your best bet tends to be something with a Turing nVidia GPU w/ NVENC support, so GTX 1650 Super or newer/higher. I think the same applies for laptop or desktop (not 100% sure on that)
That said, most monitors have multiple video inputs, so you wouldn't necessarily need another monitor. I find switch inputs on my brand new 32" 1440p monitor a bit tedious compared to my almost 20 yr old 20" Ultrasharp where I can cycle through video inputs quickly and easily from a single button on the front panel.. or there are always KVM switchers
Are you planning for Windows PC/laptop to ONLY be running OBS, ie streaming content from other device (Mac or gaming console)? in which case, what is your plan for video capture/transfer? to use HDMI capture card, or NDI, or ??
I'm surprised an i9 MacBook is struggling, but depends on what you are doing and what you are expecting in terms of video quality. Did you see the article on the guy annoyed by his MacBook fan so removed bottom and set up a liquid cooling setup and greatly improved performance (by changing thermal thresholds).. anyway... Are you gaming on the Mac and trying to stream from it?
Sorry, not a Mac person... I've heard in general that AMD's GPU encoding offload isn't that good (Windows side), is it the same on the Mac side? Are you gaming or other on the Mac, and trying to stream? or just streaming content from gaming console? if just doing video capture/real-time video encoding/streaming, I'd have thought the MacBook would be ok (assuming realistic stream settings for a laptop)
Not sure about in British pound market, but here in US dollars, lots of perfectly usable gaming laptops for streaming in the US$1->1.5K range. Real-time video encoding is demanding, so I'd recommend looking for the Turing or Ampere NVENC option (assuming that video quality is ok for you), or a laptop capable of providing a high level of cooling to the CPU (good to have regardless)