Reorganize folders, samples, minor bug fix (#14)

Reorganize folders
Samples
Casing fixes

src/mcpdotnet/Protocol/Types/Root.cs

@@ -8,15 +8,18 @@ public class Root
     /// <summary>
     /// The URI of the root.
     /// </summary>
+    [System.Text.Json.Serialization.JsonPropertyName("uri")]
     public required string Uri { get; init; }
 
     /// <summary>
     /// A human-readable name for the root.
     /// </summary>
+    [System.Text.Json.Serialization.JsonPropertyName("name")]
     public string? Name { get; init; }
 
     /// <summary>
     /// Additional metadata for the root. Reserved by the protocol for future use.
     /// </summary>
+    [System.Text.Json.Serialization.JsonPropertyName("meta")]
     public object? Meta { get; init; }
 }