Found a fix

In eslintrc.js:

plugins: [
    'html',
    'import',
  ],
  settings: {
    'import/core-modules': [ 'quasar' ],
  },

install npm module eslint-plugin-import

It seems to be caused by eslint being unaware of the alias in config/index.js

I switched my eslint config to airbnb, because I prefer the style over standard.

This causes an error in imports from quasar.

To reproduce:

quasar init test
cd test
npm install
npm install -s eslint-config-airbnb-base

Then in your .eslintrc.js file, change:
extends: 'standard' to extends: 'airbnb-base'

I get this error:

/home/elco/repos/quasar-template/src/components/Error404.vue
  35:1   error  'quasar' should be listed in the project's dependencies. Run 'npm i -S quasar' to add it  import/no-extraneous-dependencies
  35:29  error  Unable to resolve path to module 'quasar'                                                 import/no-unresolved
  35:29  error  Missing file extension for "quasar"                                                       import/extensions

This is with the standard template, I only changed the linter. I can obviously install quasar, but that resolves to this (https://www.npmjs.com/package/quasar), which is not the right thing.

How can I make eslint understand the imports from quasar?

PS: I use this to automatically fix linting errors (also makes switching from standard to airbnb easier):

In package.json, add this line to scripts:
"lint-fix": "eslint --fix --ext .js,.vue src"

Now you can fix your linting errors by running: npm run lint-fix