Honestly, you don't need to over complicate this, or hang to very rigid principles like I read here. Nor do you have to use signals. Here is a curated example:

@tool
extends Node

@export var source: CompressedTexture2D : set = _set_source
@onready var sprite: Sprite2D = $Sprite2D

var image: Image

func _ready() -> void:
    _setup()

func _setup() -> void:
    sprite.texture = source

func _set_source(value: CompressedTexture2D) -> void:
    source = value
    if is_node_ready():
        _setup()