The CPU/GPU usage for streaming depends mostly on the encoder that you're using. Programs like OBS allow you to use different encoders with different settings. This will place a very different load on your system. Eg x264 slow at 1080p would use a lot of CPU resources on most CPUs. On the other hand, if you have an nvidia GPU capable of nvenc and use that then you get next to no CPU usage. Same goes if you have an Intel CPU with an iGPU and use QuickSync or AMD's GPU encoder.

I'll say that even most modern desktop CPUs would use about a CPU core when encoding x264 even on fast preset at 1080p. It's pretty CPU intensive. That's why hardware encoders such as nvenc are popular. You most likely want to check what kind of encoder you're using. Maybe there are no other options than x264. In that case you might want to drop encoder settings and perhaps the resolution.