You can also manually use the parser to convert a Markdown text into a TextAsset or a string in RichText format to display it with
TextMeshPro.

using MarkdownToUnity.Runtime;

UnityUIMarkdownTextAsset asset = MarkdownUnityParser.ParseMarkdown(markdownText);

The asset contains all the elements to be rendered. Example functions can be found in the MarkdownUnityRenderer class.
For asynchronous calls, you can use coroutines or UniTask:

using MarkdownToUnity.Runtime;

// One instance per place you render into - it holds the current render
// state, so don't share a single instance across simultaneous renders.
private readonly MarkdownUnityRenderer renderer = new MarkdownUnityRenderer();

private IEnumerator Test(TextAsset markZip, string languageMarker)
{
    if (spinner != null) spinner.SetActive(true);

    Task<UnityUIMarkdownTextAsset> parseTask = MarkdownUnityParser.ParseMarkdown(markZip, languageMarker);
    yield return new WaitUntil(() => parseTask.IsCompleted);

    if (parseTask.IsFaulted)
    {
        Debug.LogError($"Exception: {parseTask.Exception?.InnerException?.Message}");
    }
    else
    {
        UnityUIMarkdownTextAsset asset = parseTask.Result;
        if (asset != null)
        {
            renderer.Render(asset, content, textPrefab.gameObject, horizontalLinePrefab, blockquotePrefab, codeBlockPrefab);
            // Or your own rendering logic
        }
    }

    if (spinner != null) spinner.SetActive(false);
}

MarkdownUnityRenderer is a plain class, not static — each instance owns its own style settings and render state, so several can render or stream independently at the same time without interfering with each other.