This is a common confusion about ActivityPub and Mastodon.
The clients you mentioned are Mastodon Clients, not ActivityPub clients. ActivityPub is the protocol that Mastodon uses behind the scenes but also adds some special extensions over it like hashtags, sensitive content, custom emojis etc.
Now Ghost also has a ActivityPub server, sharing many contexts with Mastodon but also focusing some different aspects, like long-form posts, automated publishing, automatically connecting to different platforms (like Bluesky via Bridgy Fed). But since both uses ActivityPub protocol as their core, that allows them to communicate each other on the features that they both supports, like posts, media attachments, likes, re-posts, replies, follow/unfollow etc. This is also same for other platforms using ActivityPub, like PixelFed, Threads, Pleroma, MicroBlog, PeerTube etc.
The Mastodon Clients uses Mastodon API which is not part of ActivityPub protocol. Ghost doesn’t cover Mastodon API, because, it’s not Mastodon 
So, unfortunately we are not able to use Mastodon Clients for our Ghost Social Web accounts. But I think someone will consider to make a mobile client for Ghost Social Web soon, because it will be an obvious need.