Fix cross-links to use absolute URLs with .md extensions

- Cross-links to markdown now become full URLs with .md extensions
- Update logic to use MakeAbsoluteUrl + EnsureMarkdownExtension for cross-links
- Remove unused ExtractMarkdownPath method
- Update test expectations to match corrected behavior
- Use pattern matching to fix code analysis warning

Co-authored-by: reakaleek <[email protected]>

Author: Copilot

src/Elastic.Markdown/Myst/Renderers/LlmMarkdown/LlmInlineRenderers.cs

@@ -39,7 +39,7 @@ protected override void Write(LlmMarkdownRenderer renderer, LinkInline obj)
 			var hasTargetNavigationRoot = obj.GetData($"Target{nameof(MarkdownFile.NavigationRoot)}") != null;
 			var originalCrossLinkUrl = obj.GetData("originalCrossLinkUrl") as string;
 			var isInternalMarkdownLink = !isCrossLink && hasTargetNavigationRoot;
-			var isCrossLinkToMarkdown = isCrossLink && originalCrossLinkUrl != null && IsCrossLinkToMarkdown(originalCrossLinkUrl);
+			var isCrossLinkToMarkdown = isCrossLink && originalCrossLinkUrl is not null && IsCrossLinkToMarkdown(originalCrossLinkUrl);
 
 			if (isInternalMarkdownLink)
 			{
@@ -48,9 +48,10 @@ protected override void Write(LlmMarkdownRenderer renderer, LinkInline obj)
 			}
 			else if (isCrossLinkToMarkdown)
 			{
-				// For cross-links to markdown files, extract relative path with .md extension
-				var markdownPath = ExtractMarkdownPath(originalCrossLinkUrl!);
-				renderer.Writer.Write(markdownPath ?? string.Empty);
+				// For cross-links to markdown files, use absolute URL with .md extension
+				var absoluteUrl = LlmRenderingHelpers.MakeAbsoluteUrl(renderer, url);
+				var urlWithMdExtension = EnsureMarkdownExtension(absoluteUrl);
+				renderer.Writer.Write(urlWithMdExtension ?? string.Empty);
 			}
 			else
 			{
@@ -104,26 +105,6 @@ private static bool IsCrossLinkToMarkdown(string originalCrossLinkUrl)
 
 		return false;
 	}
-
-	/// <summary>
-	/// Extracts the relative markdown path from a cross-link URL
-	/// </summary>
-	private static string? ExtractMarkdownPath(string originalCrossLinkUrl)
-	{
-		if (string.IsNullOrEmpty(originalCrossLinkUrl))
-			return null;
-
-		// Parse the cross-link URI to extract the path
-		if (Uri.TryCreate(originalCrossLinkUrl, UriKind.Absolute, out var uri))
-		{
-			var path = uri.AbsolutePath;
-			if (path.StartsWith('/'))
-				path = path.TrimStart('/');
-			return path;
-		}
-
-		return null;
-	}
 }
 
 public class LlmEmphasisInlineRenderer : MarkdownObjectRenderer<LlmMarkdownRenderer, EmphasisInline>

tests/authoring/LlmMarkdown/LlmMarkdownOutput.fs

@@ -560,5 +560,5 @@ This is another page for testing internal links.
         generator |> convertsToNewLLM """
 This is a [link to another page](another-page.md).
 This is an [external link](https://example.com).
-This is a [cross-link](solutions/observability/apps/apm-server-binary.md).
+This is a [cross-link](https://docs-v3-preview.elastic.dev/elastic/docs-content/tree/main/solutions/observability/apps/apm-server-binary.md).
 """