should i record my screen at a lower than 1080p screen resolution?

If my thinking is right, it's going to scale it up, so you'll have bigger text but less clarity?

Why not, just make a few seconds of video and export it to test?

That would be the first step anyways to ensure that all settings are correct before you commit to doing all your course videos.

Daniel is right. In general, you want to avoid upscaling.

You might get away with it when the viewer watches the video on a small screen. However, when you watch it full screen, you'll see that the image becomes fuzzy and you'll get some unwanted artifacts as a bonus (like more moiré). On top of that, you are most probably going to transfer your final video to a compressed format. What happens when you render a picture at an original resolution of 1280 and then upscale it to 1920 or even 2K? Do you lose information? No. The image is simply stretched to cover a higher screen resolution.

You might get away with a smaller resolution gap, e.g. 1600 to 1920. And there are some techniques to get a better image quality when upscaling, but i.m.o. you'll never get it perfect. Personally, I think that one can better use an original NTSC or PAL resolution, than upscale a lower resolution to HD. But that's just my opinion.

If you want to create a good viewer experience, make sure the text on screen is easily readable (accompanied by a voice if you like) and offer a superior image quality.

Use larger font size!

Try to use any screen recording software like camtasia, to test the different result quality than powerpoint video feature.

Try to design your slide (all text & images) as a high-resolution image/photo in higher pixel size than 1080p in highest JPG compression format. Then use it in your power point.

Hope it helps.