vscode.languages.registerCompletionItemProvider not working with 'markdown'

I am trying to write a VS Code extension to provide a completion provider in markdown, but following the example from Microsoft from this repo I can't seem to get things working when I switch the language from 'plaintext' to 'markdown'.

With the following code, with my extension running in debug mode, in a .txt file typing "h" will trigger the completion suggestions, but it won't trigger completions when in an .md file.

Am I making some sort of silly mistake here?

import * as vscode from 'vscode';

export function activate(context: vscode.ExtensionContext) {
  console.log('activate');

  let _provideCompletionItems = {
    provideCompletionItems(
      document: vscode.TextDocument,
      position: vscode.Position,
      token: vscode.CancellationToken,
      context: vscode.CompletionContext
    ) {
      console.log('provide');
      const c = new vscode.CompletionItem('Hello World!');
      return [c];
    },
  };


  context.subscriptions.push(
    vscode.languages.registerCompletionItemProvider('plaintext', _provideCompletionItems)
  );

  context.subscriptions.push(
    vscode.languages.registerCompletionItemProvider('markdown', _provideCompletionItems)
  );

  const md = { scheme: 'file', language: 'markdown' };
  context.subscriptions.push(
    vscode.languages.registerCompletionItemProvider(md, _provideCompletionItems)
  );
}