Enhance documentation to clarify Xeus-Python foundation, connection methods, and cross-platform support for DataLab-Kernel

Author: PierreRaybaut

doc/index.rst

@@ -68,9 +68,17 @@ notebook-based workflows for signal and image analysis with
 Key Features
 ------------
 
+**Xeus-Python Foundation**
+    Built on `Xeus-Python <https://github.com/jupyter-xeus/xeus-python>`_ for
+    improved performance, native debugger support, and excellent Qt event loop integration.
+
 **Dual Operating Modes**
     - **Standalone mode**: Work independently with HDF5 persistence
-    - **Live mode**: Synchronize with running DataLab instance via XML-RPC
+    - **Live mode**: Synchronize with running DataLab via Web API (recommended) or XML-RPC
+
+**Cross-Platform Jupyter Support**
+    Works in native Jupyter (JupyterLab, Notebook, VS Code) and
+    `JupyterLite <https://jupyterlite.readthedocs.io/>`_ (browser-based, no server required).
 
 **Unified API**
     Same code works in both modes - switch seamlessly between local notebooks

doc/user_guide/features.rst

@@ -186,18 +186,30 @@ Jupyter Integration
 
 Works seamlessly with:
 
+**Native Jupyter environments:**
+
 - **Jupyter Notebook**: Classic notebook interface
 - **JupyterLab**: Modern lab environment
 - **VS Code**: With Jupyter extension
 
-Register the kernel once:
+**Browser-based:**
+
+- **JupyterLite**: No server required, runs entirely in the browser via WebAssembly
+
+For native environments, register the kernel once:
 
 .. code-block:: console
 
     $ datalab-kernel-install
 
 Then select "DataLab" kernel in any Jupyter frontend.
 
+For JupyterLite, load the extension in your notebook:
+
+.. code-block:: python
+
+    %load_ext datalab_kernel
+
 
 Error Handling
 --------------

doc/user_guide/overview.rst

@@ -80,13 +80,18 @@ This mode is ideal for:
 Live Mode
 ^^^^^^^^^
 
-When DataLab is running, the kernel connects via XML-RPC:
+When DataLab is running, the kernel connects via Web API or XML-RPC:
 
 - Objects synchronized with DataLab panels
 - Access to DataLab's full processing pipeline via ``calc()``
 - Direct proxy access for advanced operations
 - Changes visible in real-time in DataLab GUI
 
+Two connection methods are supported:
+
+- **Web API** (recommended): HTTP/JSON connection, WASM/Pyodide compatible
+- **XML-RPC** (legacy): Automatic connection when DataLab has remote control enabled
+
 This mode enables:
 
 - Interactive exploration with GUI feedback