There are lots of online texture packers but they always re-arrange the order in some arbitrary order, then provide the ordering info in a JSON or other metadata file. The problem is when importing into Unity, Unity does its own splicing using the splicing sprite editor, which has some options such as “grid”, which expects a perfectly ordered left-to-right top-to-bottom, and doesn’t read these JSON files. So when importing into Unity, the output of CodeAndWeb etc texture packers will always be out of order.
If you want the easiest solution don’t mess with third party packers. Just import your individual pngs directly in Unity and use the Unity builtin sprite atlas Unity - Manual: Sprite Atlas .
If you really want to use an external sprite packer to achieve slightly better packing and geometry, choose a good sprite packer which provides a unity extension for importing the sprite sheet it export. For example CodeAndWeb you mentioned as example has one, it’s explained in their tutorial https://www.codeandweb.com/texturepacker/tutorials/how-to-create-a-2d-game-scene-in-unity .
If you want to use a third party sprite packer which doesn’t provide an extension for importing it’s format, then you will have write one yourself. I don’t recommend doing this unless you have a very good reason and the skills for it.