How attach a Custom Field do it by code to a Custom Type Page
You just have to create or change the file attaching the field to instead be attached to the page content type:

First we'll have to rename it: field.field.node.page.field_brand_information.yml

Secondly, we should be fine just changing all the references from car_brand to the page bundle instead:

# field.field.node.page.field_brand_information.yml
langcode: en
status: true
dependencies:
  config:
    - field.storage.node.field_brand_information
    - node.type.page
  module:
    - text
id: node.page.field_brand_information
field_name: field_brand_information
entity_type: node
bundle: page
label: 'Brand Information'
description: 'More specific information about the car brand'
required: false
translatable: false
default_value: {  }
default_value_callback: ''
settings:
  display_summary: false
field_type: text_with_summary


Generally this approach is quite tedious and I agree as also pointed out in the article that you rather do it through the UI and then export the files appropriately.