Can you try this repo I've just created? Looks like it's working great from what I've tested.

https://github.com/kissu/stackoverflow-eslint-standard-prettier-config

Notes

• I created 2 projects and dumped the configuration of the standard one into the Prettier one
• CLI's current version of @vue/eslint-config-standard is throwing an error (Environment key "es2021" is unknown) because it requires ESlint 7 to work, as shown in this changelog
• bumping ESlint to the latest version 7.29.0, fixed the issue
• to check your project's current version of ESlint, you can run npx eslint --version
• of course, you need to have the ESlint extension enabled and Prettier one disabled (if using VScode), otherwise it may conflict

I've tried to remove @vue/prettier from

extends: ['plugin:vue/essential', 'eslint:recommended', '@vue/standard', '@vue/prettier']

and see if it's successfully removes any ; and it does!

The errors are indeed coming from ESlint (if we do remove @vue/prettier), and they're fixed by ESlint only upon save (after an ESlint server + VScode restart)!

Putting Prettier back works fine of course.

Luckly, I had a new PC, hence had the opportunity to try a whole fresh config with VScode. I had to install ESlint only and have those settings into my settings.json

{
  "editor.codeActionsOnSave": {
      "source.organizeImports": false,
      "source.fixAll": true,
      "source.fixAll.eslint": true,
      "source.fixAll.stylelint": true
    }
}

The formatting works perfectly and nothing more is required.

According to a blog post I found [1] these steps should make it sure it works:

1. Download the ESLint and Prettier extensions for VSCode.

2. Install the ESLint and Prettier libraries into our project. In your project’s root directory, you will want to run:

npm install -D eslint prettier

3. Install the Airbnb config. If you’re using npm 5+, you can run this shortcut to install the config and all of its dependencies:

npx install-peerdeps --dev eslint-config-airbnb

4. Install eslint-config-prettier (disables formatting for ESLint) and eslint-plugin-prettier (allows ESLint to show formatting errors as we type)

npm install -D eslint-config-prettier eslint-plugin-prettier

5. Create .eslintrc.json file in your project’s root directory:

{
  "extends": ["airbnb", "prettier"],
  "plugins": ["prettier"],
  "rules": {
    "prettier/prettier": ["error"]
  },
}

6. Create .prettierrc file in your project’s root directory. This will be where you configure your formatting settings. I have added a few of my own preferences below, but I urge you to read more about the Prettier config file

{
  "printWidth": 100,
  "singleQuote": true
}

7. The last step is to make sure Prettier formats on save. Insert "editor.formatOnSave": true into your User Settings in VSCode.

[1] https://blog.echobind.com/integrating-prettier-eslint-airbnb-style-guide-in-vscode-47f07b5d7d6a

vue/script-indent (ESLint rule)

From the eslint-plugin-vue docs:

Create .eslintrc.* file to configure rules. See also: http://eslint.org/docs/user-guide/configuring.

Example .eslintrc.js:

module.exports = {
  extends: [
    // add more generic rulesets here, such as:
    // 'eslint:recommended',
    'plugin:vue/essential'
  ],
  rules: {
    // override/add rules settings here, such as:
    // 'vue/no-unused-vars': 'error'
  }
}

So in your .eslintrc.js, add the script-indent rule to the rules property. Note the eslint-plugin-vue rule names are all prefixed with vue/, so use "vue/script-indent" in the rules property below:

module.exports = {
  extends: [
    'plugin:vue/essential',
  ],
  rules: {
    'vue/script-indent': ['error', 2, {
      baseIndent: 0,
      switchCase: 0,
      ignores: []
    }]
  }
}

Finally, ensure you have the ESLint VS Code extension installed to enable formatting from the IDE.

Prettier

Your workspace settings point to Prettier, so make sure your Prettier options align with the vue/script-indent rule. That is, the tabWidth value in Prettier should match the tab width in vue/script-indent.

For example, to require a 4-space tab width, create .prettierrc in the root of your project with the following JSON:

// .prettierrc
{             
  "tabWidth": 4
}

...and update .eslintrc.js to match:

// .eslintrc.js
module.exports = {
  rules: {                         
    'vue/script-indent': ['error', 4, {
      baseIndent: 0,
      switchCase: 0,
      ignores: []
    }]
  }
}

Also ensure you have the Prettier VS Code extension installed to enable formatting from the IDE.