docs: fix stub pages and improve docs structure (#2101)

Co-authored-by: Max Isbey <224885523+maxisbey@users.noreply.github.com>

examples/snippets/clients/stdio_client.py

@@ -62,7 +62,7 @@ async def run():
             # Read a resource (greeting resource from fastmcp_quickstart)
             resource_content = await session.read_resource(AnyUrl("greeting://World"))
             content_block = resource_content.contents[0]
-            if isinstance(content_block, types.TextContent):
+            if isinstance(content_block, types.TextResourceContents):
                 print(f"Resource content: {content_block.text}")
 
             # Call a tool (add tool from fastmcp_quickstart)