I don't know why this happens, but I realized it also happens when the game is running and I slow down to a full stop as the character (with the player camera only rocks and gems shake).
This happens also with ObstacleCourse_Part3 without me editing anything inside it. I think it has to do with how Godot is set up on my PC or just my graphics card or something.
Here's a drive link to a screen recording I did: ScreenShake
I realized that if I turn off GPU pixel snap, the shaking stops, but then lines would appear between the tiles when moving the character/camera
I see, so it seems that the GPU pixel snap is causing the issue on your computer. This is really unfortunate. We won't have a good workaround for that, as we use pixel snap to avoid the lines between tiles, as you observed.
In Godot 4 there's a tool built-in that will remove these lines between tiles issue, which you face in almost every game engine. It's due to a sampling imprecision on the graphics card's side when we don't snap pixels in the game to pixels on the screen.
You can give special treatment to the tileset texture to get rid of the issue, but surprisingly there aren't many tools to help you do that as we have a limited budget, and this is a visual glitch GPU snapping normally solves for... almost everyone it seems, we decided we just wait for Godot 4, which has it built-in.