I decided to remove everything eslint related in the website project and installed eslint-config-next in the root project:

env:
  es2021: true
  shared-node-browser: true

extends:
  - eslint:recommended
  - plugin:@typescript-eslint/recommended
  - next/core-web-vitals
  - prettier

parser: "@typescript-eslint/parser"

parserOptions:
  sourceType: module

plugins:
  - "@typescript-eslint"
  - import

settings:
  next:
    rootDir: "./website"

rules:
  no-duplicate-imports: error
  no-template-curly-in-string: warn
  no-unreachable-loop: warn
  camelcase: error
  curly: error
  eqeqeq: error
  no-console: error
  no-else-return: error
  no-empty-function: error
  no-eval: error
  no-new: error
  no-param-reassign: error
  no-return-await: warn
  no-unneeded-ternary: error
  no-useless-rename: error
  no-var: error
  prefer-arrow-callback: error
  prefer-const: error
  prefer-destructuring: error
  prefer-object-spread: error
  prefer-template: error
  block-spacing: error
  padding-line-between-statements:
    [error, { blankLine: "always", prev: "*", next: "return" }]
  "@typescript-eslint/explicit-module-boundary-types": off
  "@typescript-eslint/no-shadow": error
  import/order:
    [
      error,
      {
        alphabetize: { caseInsensitive: true, order: asc },
        groups: [[external, builtin], internal, parent, sibling, index],
        newlines-between: never,
      },
    ]

I'm not using next lint this way but linting should work fine this way, if I can get some nicer integration I'd be open to suggestions