ESLint + Prettier formatOnSave does work but not Alt + Shift + F

I've created a separate repo with shared eslint config for different projects in my org:

module.exports = {
  parser: '@typescript-eslint/parser', // Specifies the ESLint parser
  extends: [
    'airbnb-base',
    'plugin:@typescript-eslint/recommended',
    'prettier',
    'plugin:import/errors',
    'plugin:import/warnings',
    'plugin:import/typescript',
    'plugin:jest/recommended',
    'plugin:prettier/recommended',
  ],
  plugins: ['@typescript-eslint', 'jest', 'prettier'],
  parserOptions: {
    ecmaVersion: 12,
    sourceType: 'module',
  },
  env: {
    node: true,
    es6: true,
    jest: true,
  },
  rules: {
    'eol-last': ['error', 'always'],
    'newline-before-return': 'error',
    'import/extensions': 0,
    'import/no-extraneous-dependencies': [
      'error',
      {
        devDependencies: false,
        optionalDependencies: false,
        peerDependencies: false,
      },
    ],
    'no-restricted-imports': [
      'error',
      {
        patterns: [
          {
            group: ['.prisma/*'],
            message: 'Use @prisma instead of .prisma',
          },
        ],
      },
    ],
    'semi': 'error',
    'comma-dangle': 'off',
    '@typescript-eslint/comma-dangle': ['error', 'always-multiline'],
    'indent': 'off',
    'quotes': 'off',
    '@typescript-eslint/quotes': [
      'error',
      'single',
      {
        allowTemplateLiterals: true,
      },
    ],
    '@typescript-eslint/no-shadow': ['error'],
    'arrow-parens': ['error', 'always'],
    '@typescript-eslint/indent': [
      'error',
      2,
      {
        /**
         * This should stay here until https://github.com/typescript-eslint/typescript-eslint/issues/1824 is fixed
         * as currently it forces you to add additional double-space indent to function arguments with decorators
         */
        ignoredNodes: ['FunctionExpression'],
        SwitchCase: 1,
      },
    ],
    '@typescript-eslint/no-non-null-assertion': 'off',
    '@typescript-eslint/no-unused-vars': [
      'warn',
      {
        argsIgnorePattern: '^_',
      },
    ],
    'spaced-comment': ['error', 'always'],
    'no-multiple-empty-lines': [
      'error',
      {
        max: 2,
        maxEOF: 0,
      },
    ],
    'import/order': [
      'error',
      {
        'groups': [['external', 'internal', 'builtin'], ['sibling', 'parent'], 'index', 'object'],
        'pathGroupsExcludedImportTypes': ['builtin'],
        'newlines-between': 'always',
        'alphabetize': {
          order: 'asc',
          caseInsensitive: true,
        },
      },
    ],
  },
  settings: {
    'import/resolver': {
      node: {
        extensions: ['.js', '.ts', '.jsx', '.tsx'],
      },
    },
  },
  overrides: [
    {
      files: ['*.ts', '*.tsx'],
      rules: {
        'no-undef': 'off',
      },
    },
    {
      files: ['next.config.js'],
      rules: {
        '@typescript-eslint/no-var-requires': 'off',
      },
    },
  ],
};

Then I published this package to my private registry and installed it on the other repository where I used it to extend from in that repo's eslint config:

module.exports = {
  extends: '@flaut-org/eslint-config',
  ignorePatterns: ['.eslintrc.js'],
  rules: {
    'import/order': [
      'error',
      {
        'groups': [['external', 'internal', 'builtin'], ['sibling', 'parent'], 'index', 'object'],
        'pathGroups': [
          {
            pattern: '@nestjs/**',
            group: 'external',
            position: 'after',
          },
        ],
        'pathGroupsExcludedImportTypes': ['builtin'],
        'newlines-between': 'always',
        'alphabetize': {
          order: 'asc',
          caseInsensitive: true,
        },
      },
    ],
  },
};

But for some reason autoformatting didn't work in VSCode. I've configured my default formatter to be Prettier - Code formatter and retried - didn't do the trick. Then I've added the following lines to my ./vscode/settings.json config:

{
    "eslint.validate": [
        "javascript",
        "typescript"
    ],
    "editor.codeActionsOnSave": {
        "source.fixAll.eslint": true
    },
    "[typescript]": {
        "editor.defaultFormatter": "esbenp.prettier-vscode"
    },
}

And VSCode actually started auto-formatting it on Ctrl + S, but Alt + Shift + F combination still doesn't work. I've checked both Prettier and ESLint logs and there were no errors and warnings whatsoever. What am I missing that does not allow me to use Alt + Shift + F combination ?