Are you getting a 404 for the .json or the textures?
I think you have to set the path first, otherwise the textures will be loaded from the root folder.
I have this working with multiatlas and webpack 4.20.4.
I build my files into ./dist and I publish my TexturePacker multiatlas into ./dist/img/assets.
Loading the atlas with scene.load.multiatlas('key', './dist/img/assets/file.json);
The catch, is that the TexturePacker texturepath property doesn’t work, so I had to do a find/replace within the json file to add the './dist/img/assets/' path in front of the image property. In my case I have sd,md,hd variants, so three json files. Adding the path in the json files fixes the issue, other wise the images are loaded from the project root.