DataLake to DataWarehouse

You could perhaps use Dataflows Gen2 with Append method.

Pattern to incrementally amass data with Dataflow Gen2 - Microsoft Fabric | Microsoft Learn

This should work similarly both for Lakehouse or Warehouse.

Or just use a cross-database query to get the Lakehouse data into your Warehouse, as shown in the previous comment (however it doesn't work for Lakehouse files, only Lakehouse tables).

I don't think Notebook can write data to Warehouse. So I don't think what you are asking is directly possible.
I think you will need to use some other tool than Notebook (Dataflows Gen2, T-SQL script or stored procedure, data pipeline, etc.).
Or you can use Notebook to enter data into a Lakehouse table, and then use cross-database queries to make the data available in the Warehouse.

If you want to use Notebook to load data, why not just use Lakehouse instead of Warehouse?  I am curious.

If someone knows how to use Notebook to write data to Warehouse, I am interested to know.

Right now we can't write to a Warehouse without going through the Warehouse SQL Endpoint (we can read via Spark as you know).  So the only way to work with data is using a connectivit method like pyodbc and connecting to the Warehouse SQL Endpoint in the Notebook.

I'll dig up an example I did a whle ago to show this.

Connectivity to data warehousing - Microsoft Fabric | Microsoft Learn