Does Ghost Still Have a Markdown Editor? Yes, as a Card Inside the Block Editor
Yes, as a card. Ghost's editor is a block editor, and one of its blocks is a Markdown card. Ghost's own markdown guide draws the line: the editor "automatically parses any Markdown typed in directly", and "If you want to keep your content formatted in Markdown for editing later, or you'd like to include footnotes in your post, then you can also use the Markdown card." So markdown typed anywhere else in a post is converted into the editor's own formatting as you type it, and only markdown typed inside the card stays markdown.
If you remember Ghost as a markdown blogging app, that is the answer in one line. The rest of this post is what it means when you want the post itself, not one block of it, to be markdown.
What changed since the v1 markdown editor
The block editor was there before the card was. The Ghost 1.0 announcement, in July 2017, said that "the upgraded Markdown editor is just a content block within the new Koenig editor". Ghost 2.0, in August 2018, then made the block editor the default: "For the first time since we started, Markdown is no longer the default way to write in Ghost (although it's very much still available)", and "Our old Markdown editor is now a card within the new editor".
The full account of that move, from the original split-screen editor to the card, is in Ghost CMS alternative with a markdown editor, so this post does not retell it.
What is and is not markdown once a post has cards
Inside a Markdown card, the text is markdown, and Ghost's guide says the card is how you "keep your content formatted in Markdown for editing later". Footnotes only work there: "To add footnotes using the Ghost editor, insert a Markdown card into your post", and they "will always appear beneath the markdown card" on the published page (using markdown).
Outside the card, markdown is a typing shortcut. The cards reference puts it in one sentence: "Ghost automatically parses Markdown when typed directly into the editor, or you can use the Markdown card to create full posts in Markdown or use footnotes." A forum moderator answering a writer who missed the old editor said the same thing from the other side: the new editor converts "markdown to rich text as you type". Once it has been converted, there is no markdown to go back to.
The post is not stored as markdown either. In the Admin API's create-a-post example, the body is a lexical field holding a JSON document. So a post that mixes a Markdown card with a heading, a paragraph and an image typed outside it is one Lexical document with some markdown in one of its nodes. Ghost's help pages do not say how the card's text sits inside that document, so this post does not either.
The same holds on the way out. Ghost's export is "Content (posts and pages) in a JSON format": from Settings → Advanced → Import/Export you "download your posts and settings in a single JSON file" covering all settings, staff users, posts, pages and tags. Blognami, which this blog runs on, does it the other way round. On the hosted version an admin chooses Settings → Export content and gets a zip with one markdown file per post and per page, the title, slug, tags and meta fields as frontmatter, and beneath it the body exactly as it was typed, drafts included. Its limits are that uploaded images are not in the zip, and that the export is part of the hosted product, not the open-source code, where the markdown sits in your own database instead.
Where to look if markdown has to be the document
If what you want is for the post itself to be markdown, look for a platform that stores the body as markdown text and renders it when the page is served, with no block document in between. The test is simple: write a post, save it, reopen it, and see whether you get back exactly what you typed.
Blognami is one option, and since you are reading this on its blog, weigh that accordingly. A post's body is a single markdown text, rendered to HTML when the post is displayed. The editor opens as a modal over the post's body field, with the markdown on the left and a live preview on the right, rendered by the same renderer the published post uses. Side-by-side is a desktop-width behaviour: on a narrow screen the two panes collapse into an Edit / Preview toggle. The panes do not scroll in sync, and there is no Ghost importer, so moving posts across is copy and paste. The docs cover what it is and how to run it yourself.