If you are looking to automatically post your Mastodon posts to your Ghost blog or have them appear as a sidebar, the simplest way to accomplish this may be to use the RSS feeds are available for every user.
Just add “.rss” to the URL for your profile to find your feed! From there, the existing resources you can find about using RSS with Ghost will apply. For example, here’s an old forum thread about automatically publishing entries from an RSS feed as Ghost posts:
Any resource you find for embedding RSS entries as a sidebar in Ghost would also work for Mastodon posts this way.