It sounds like you want to create an application where its business logic executes on the public Ethereum network, this is not possible with Daml. Daml code executes alongside distributed ledgers/blockchains and uses them for data persistence and consensus but not execution.
The extension you’re using here is for Visual Studio Code which is an extendable code editor/IDE that has support for many programming languages. Daml Studio is also an extension for Visual Studio Code but it has nothing to do with Solidity or other extensions.