Whenever I move my 2D Camera around (when smoothing is enabled), the sprites seem to shake, which is visually distracting - is there any way to disable this?
Enabling these two options should help you:
These options are under Project Settings, with "Advanced Settings" enabled in Rendering / 2D.
Godot 4 removed the old GPU Pixel Snap and replaced it with this to break it down into more specific GPU-agonistic options.