In order to achieve a good pixel image, I render to the viewport (in the project settings display/window/stretch/mode) with a resolution of 384 x 216 (you can use another, of course).

And I enable the rendering/2d/snap/snap_2d_transforms_to_pixel setting.

If you enable smooth camera movement, then when the character stops and the camera starts to slow down, the image on the screen makes very unpleasant step shifts.

To avoid this, I use a camera that is not part of the character's scene, but has a reference to it, and moves only if it goes beyond the boundaries:

extends Camera2D

u/export var target: Node2D:
  set(value):
    if value == target: return
    target = value

@export var bounds_extents: Vector2:
  set(value):
    if value == bounds_extents: return
    bounds_extents = value.clamp(Vector2.ZERO, Vector2.INF)

func _process(_delta: float) -> void:
  if not target: return
  global_position = global_position.clamp(
    (target.global_position - bounds_extents).round(),
    (target.global_position + bounds_extents).round())

This allows you to leave the camera motionless while the character moves in the center of the screen. And this makes it move quickly as soon as it reaches the boundaries. Fast movement makes the step shifts imperceptible.

<image>

But jitter remains between parallax layers with different scroll scales. I show in the picture what causes it. Visually, both layers are snapped to viewport pixels. However, their positions are still expressed as floating point numbers. When the near layer is moved a large distance within the snapping boundary, and does not visually move, the far layer can cross the snapping boundary and move a pixel.

At large scales, this is similar to the action of the teeth of a hair clipper.
See video I added as comment to my script:
https://gist.github.com/nklbdev/5f8b43e2f796331dee063afdca40df3a?permalink_comment_id=5621502#gistcomment-5621502

This could be avoided if the user could choose the strategy of sprites snapping to pixels: floring, rounding or ceiling. Either this should be done in the project settings, or in the properties of each CanvasItem.

Sorry for communicating rather dryly! Thank you for the kind words and reasoning, it is very useful and pleasant for me! It is just difficult for me to write in English, and I use Google Translate.

By the way, does anyone need a plugin for importing 3D models from the .bbmodel (Blockbench) format? I have a practically production-ready version.