How can you automatically add CSS classes to  tags in the post body?
I have found how to resolve this specifically if using the Tailwind framework, which I am.

You can use the @apply function of the framework to add classes based on common Drupal class names, or ones you specify in your custom html.twig files.

Documentation here: https://tailwindcss.com/docs/functions-and-directives/#apply
I am using the Tailwind Starter theme which also uses this function https://www.drupal.org/project/tailwindcss

For example, to apply the text-xl utility class to node paragraph tags, I can use the following code in my stylesheet

.node-content p {
  @apply text-xl
}