Hi @SBL ,
Even if you use Serverless compute, they still will charge you for public connectivity connection type (as you can see at below documentation entry):
Understand Databricks serverless networking costs - Azure Databricks | Microsoft Learn

Unfortunately, I doubt that this option can be completely disabled. Serverless is managed by Databricks.
You can setup network policy to control servless egress and restrict outbound access, but I don't see any place to turn off Nat Gateway.
What you can do, assuming that your workloads don't need public internet access and that all your resources that you want to communicate with support private endpoints then you can try to configure a private connection using managed private endpoints. Then, you won't be charged by NAT Gateway usage.
If you want to have a full control just use classic compute plane networking. Then you can deploy Databricks into your own VNet and configure all networking aspects according to your needs.