Yes, it makes sense to record a higher resolution video, so you can crop part of it in postprocessing without quality loss to avoid upscaling the cropped part.
But you need to actually record this high resolution. If you record your desktop with whatever you want to present and want to include a camera video of yourself in some corner or cut the video and switch from the desktop to a fullscreen video of yourself and back, you need to record a full resolution video of your camera in addition to the full resolution video of your desktop.
So if you have your desktop with 1366x768 and your camera with 4k, and you want to composite this yourself with a postprocessing tool, you need to record both videos separately. One with 1366x768 and the other with 4k. Resizing, cropping and placing both over each other (this is called compositing) can be done in a postprocessing tool ("Video editor").
However, your laptop is too weak to make such 2 recordings simultaneously. Its even not powerful enough to record something with 4k resolution.
Some people do this: they double the frame size and put their main source next to the camera source.
For example, they want their final video be 1280x720, with a desktop recording and a camera of theirselves.
They double the canvas and output size to 1280x1440. In the upper half of that canvas, they put their desktop source with resolution 1280x720 and in the lower half of that canvas they put their camera source with also 1280x720. This can be used to record both simultaneously with OBS.
After recording, they use a video editor to separate both halves and have a 1280x720 camera video of theirselves to put wherever they like into the other half, the desktop recording.