VS Code launch.json to enable debugging of Nuxt.js apps. Note a further change is required in your nuxt.config.js

launch.json

{
  "version": "0.2.0",
  "configurations": [
    {
      "type": "chrome",
      "request": "launch",
      "name": "client: chrome",
      "url": "http://localhost:3000",
      "webRoot": "${workspaceFolder}",
      "sourceMapPathOverrides": {
        "webpack:///*": "${workspaceRoot}/*"
      }
    },
    {
      "type": "node",
      "request": "launch",
      "name": "server: nuxt",
      "args": ["dev"],
      "osx": {
        "program": "${workspaceFolder}/node_modules/.bin/nuxt"
      },
      "linux": {
        "program": "${workspaceFolder}/node_modules/.bin/nuxt"
      },
      "windows": {
        "program": "${workspaceFolder}/node_modules/nuxt/bin/nuxt.js"
      }
    }
  ],
  "compounds": [
    {
      "name": "fullstack: nuxt",
      "configurations": ["server: nuxt", "client: chrome"]
    }
  ]
}

From :
https://nuxt.com/docs/guide/going-further/debugging

{
  // Use IntelliSense to learn about possible attributes.
  // Hover to view descriptions of existing attributes.
  "version": "0.2.0",
  "configurations": [
    {
      "type": "chrome",
      "request": "launch",
      "name": "client: chrome",
      "url": "http://localhost:3000",
      "webRoot": "${workspaceFolder}"
    },
    {
      "type": "node",
      "request": "launch",
      "name": "server: nuxt",
      "outputCapture": "std",
      "program": "${workspaceFolder}/node_modules/nuxi/bin/nuxi.mjs",
      "args": [
        "dev"
      ],
    }
  ],
  "compounds": [
    {
      "name": "fullstack: nuxt",
      "configurations": [
        "server: nuxt",
        "client: chrome"
      ]
    }
  ]
}