The reason you are only seeing SQL Warehouses when clicking Compute is likely because the workspace admin has locked down interactive cluster creation. Check if you have the cluster creation entitlement. Your workspace admin can grant you the correct permissions.

You can follow below

• Job Cluster - You can use a "New job cluster" instead of selecting an existing interactive cluster or attempting to pass Serverless. When you add the notebook activity in ADF, setting it to create a new job cluster spins up ephemeral compute specifically for that run and terminates it immediately after. This mimics the cost-efficiency of serverless while remaining fully compatible with ADF's legacy notebook integration.
• Databricks Lakeflow Jobs - You can shift to Lakeflow jobs instead of having ADF orchestrate the individual notebooks. Databricks Jobs natively support Serverless compute. Once created, simply replace the ADF Notebook activities (bronze, silver notebooks etc) with a single ADF Databricks activity to trigger that Job. This routes the execution through the native Databricks plane while keeping the ADF pipeline clean.