Feature Request: Sync project to serverless.template file

Hi,
We are using the AWS Toolkit for Visual Studio 2019 to create a serverless application in .Net Core using Lambda.
When the project first gets created, a serverless.template file gets created with some basic SAM resources.
Our problem is that as we add new APIs to the project, we don't see a way of having the template file be automatically updated.

We have another team working in Node using the serverless framework and that maintains the resources automatically.
It would be great if the toolkit also did this.

Start by examining how the AWS Toolkit for Visual Studio 2019 creates the serverless.template file for .NET Core Lambda projects, then trace how newly added APIs are represented in the project. Define how synchronization should work and what serverless.template should contain after APIs are added; no test or implementation entry point is identified in the issue.

Written by the indexing model from the issue text.