A concern adapted from the GoRails ActionMailbox episode https://gorails.com/episodes/save-action-mailbox-html-emails-with-action-text?autoplay=1

mail_params.rb

# mailboxes/concerns/mail_params.rb
module MailParams
  extend ActiveSupport::Concern

  def mail_params
    attachments = build_attachments
    body = build_rich_body(attachments)
    { subject: mail.subject, body: body, attachments: attachments.map { |a| a[:blob] } }
  end

  def build_attachments
    mail.attachments.map do |attachment|
      blob = ActiveStorage::Blob.create_after_upload!(
        io: StringIO.new(attachment.decoded),
        filename: attachment.filename,
        content_type: attachment.content_type,
      )
      { original: attachment, blob: blob }
    end
  end

  def build_rich_body(attachments)
    if mail.multipart? && mail.html_part
      document = Nokogiri::HTML(mail.html_part.body.decoded)

      attachments.map do |attachment_hash|
        attachment = attachment_hash[:original]
        blob = attachment_hash[:blob]

        if attachment.content_id.present?
          # Remove the beginning and end < >
          content_id = attachment.content_id[1...-1]
          element = document.at_css "img[src='cid:#{content_id}']"

          element.replace "<action-text-attachment sgid=\"#{blob.attachable_sgid}\" content-type=\"#{attachment.content_type}\" filename=\"#{attachment.filename}\"></action-text-attachment>"
        end
      end

      document.at_css("body").inner_html.encode("utf-8")
    elsif mail.multipart? && mail.text_part
      mail.text_part.body.decoded
    else
      mail.decoded
    end
  end
end

# models/post.rb
class Post < ApplicationRecord
  has_rich_text :body
  has_many_attached :attachments
end

# mailboxes/posts_mailbox.rb
class PostsMailbox < ApplicationMailbox
  include MailParams

  def process
    Post.create mail_params
  end
end

Alright, then I guess we need to append the attachment.
Also, we may want to delete the signature.
I'll revisit that sometime later, this feature is on pause for a couple of days.