So I installed kubuntu-desktop and awesome to try other desktop environments with a different compositor but it did not change anything Godot-wise. It feels a bit smoother, maybe I'm getting more FPS, but the freezes are still are present...
@cybereality I'm using an SSD and I checked my swap file partition, I have 2 GB total but 0 GB used. It's the green line in the screenshot I shared above. So I'm guessing I have enough RAM.
@darkbean said:

I checked my RAM with memtester just in case and it reported no problems.
And finally I installed and ran intel-gpu-tools to see my GPU usage. Here are the results :
This is running Godot 3.2.1 stable on a 2D scene. (GLES 3, but got the same results with GLES 2) :

This is right after the computer unfreezes from the above scene :

This is what is looks like when running Blender 2.82a's splashscreen 3D Grease Pencil scene during a rotation. FPS drops but stays steady and no freezing :

And this is during a KSP rocket launch. FPS drops but stays steady and no freezing :

It's all really frustrating because I know Godot isn't using that much resources compared to other programs. But it's the only one I'm having issues with.