Can a laptop do real-time video encoding? Yes
But, laptops are subject to thermal throttling far more than desktops, so... buyer beware.. it depends on settings, expectations, other things running, etc. Thin and light laptops being the WORST possible type of device for real-time video encoding (but can work at lower resolutions (1080p)/settings) with optimized OS and OBS setups
If you are not technical, and especially not familiar with Windows OS optimization, then over-provisioning the hardware may be cheaper if you end up needing expensive consulting to optimize OS.
Also, the new OBS v28 (still in beta but at RC1) has native Apple Silicon M1/M2 CPU support, which may greatly improve performance (depending on settings). So first I'd ask if the OBS v28 performance meets your needs?
If not, then it really depends on what you mean by "achieving top quality video"... as that means _very_ different things to different people.
You don't mention resolution, color space, etc. So for some people, more than adequate might be a $US$1K system, and for others, they bring a $5->10K workstation to its knees. Yes, such a range of possibilities exists, hence 'it depends'. And there is typical 1080p today, but how long do you want this system to last? Will you want 4K streaming towards the end of that timeframe (or are you ok having to buy a new system to support 4K).
And most (free) livestreaming today requires H.264 (as H.265 is a licensing mess). With AV1 being the likely successor, and AV1 encode offload in GPU in latest Intel ARC GPUs, and expected in next releases of nVidia and AMG GPUs. I mention, as 'top quality' ... depends. At lower bitrates (3500kbps), current testing apparently shows AV1 significantly outperforming H.264, depending on content type. At higher bitrates, the differences appear to diminish...
Sorry, I know you were hoping for a simple answer, but your question is along the lines of 'what is the best car to get?'
