sharepoint online – Repost Page not inheriting site column when added via Site Script

I have a Site Script where I add Site Columns to the Site Pages library. My issue is when adding site columns via Site Script the Repost Page content type is not inheriting the added columns, only the Site Page content type. Adding a column via the UI works as there is an option “Add to all content types” which is missing in site script. Sample of the approach:

{
  "$schema": "https://developer.microsoft.com/json-schemas/sp/site-design-script-actions.schema.json",
  "actions": (            
    {
      "verb": "createSPList",
      "listName": "Site Pages",
      "templateType": 119,
      "subactions": (
        {
          "verb": "addSiteColumn",
          "internalName": "PageCategory",
          "addToDefaultView": true
        },
        ...
      }
    )
  }

So, I do have a solution where I instead can update the base site content type (Repost Page) however I suspect this violates good practice on what to do and not to do in SharePoint. Or, is the below OK:

    {
  "$schema": "https://developer.microsoft.com/json-schemas/sp/site-design-script-actions.schema.json",
  "actions": (
    {
      "verb": "createContentType",
      "name": "Site Page",
      "description": "Create a new site page",
      "hidden": false,
      "parentName": "Document",
      "subactions":
        (
            {
              "verb": "addSiteColumn",
              "internalName": "PageCategory"
            }           
        )
    },
    {
      "verb": "createContentType",
      "name": "Repost Page",
      "description": "Used to create a News link post. If deleted, the News link option will be disabled for users.",
      "hidden": false,
      "parentName": "Site Page",
      "subactions":
        (
          {
            "verb": "addSiteColumn",
            "internalName": "PageCategory"
          }
        )
    },        
    {
      "verb": "createSPList",
      "listName": "Site Pages",
      "templateType": 119,
      "subactions": (
        {
          "verb": "addContentType",
          "name": "Site Page"          
        },
        {
          "verb": "addContentType",
          "name": "Repost Page"
        }
        ...
      )
   }
 }

I was hoping to be able to use Site Designs/Site Scripts for this and know that alternatives exists such as PnP Provisioning etc. My hope is also to avoid creating my own Content Type.

Any thoughts on the above? Is it OK to update the base Content Type?