1. do NOT ignore the big red warning about NOT recording to MP4. (remux if you must)
2. Ah, 6 generation old ultra-low power CPU. yea, that isn't helping
15:56:36.095: Video stopped, number of skipped frames due to encoding lag: 733/2139 (34.3%)
so thermal throttling absolutely could be an issue
Your laptop is capable of recording/streaming, but with settings appropriate for an older, under-powered CPU. So to get this laptop to work, expect to take some time to learn about OS (Operating System) and OBS optimizations.
This could be simple, as the recording settings look odd to me, but then again, I haven't reviewed Mac OBS logs much, so... not sure if normal, or ??
Would a new computer be simpler? quite possibly. But as to whether required or not, I'm not sure. That will take a Mac person to respond. It could be a case of lowering recording settings, and you'll be all set. I just don't know. On the Windows side, I tried a gaming laptop, same circa 2015, with a more powerful CPU and GPU, and it didn't work for me (just starting out, I'm sure I could get it to work, just.. today). So, I suspect you'll need to be conscientious of the technical implications of your sources, your settings, what is running in the background, memory and CPU optimizations, etc Or go for newer, more powerful overkill system, and think less about those things (maybe, a M1 native OBS version hasn't been released yet).