SAM/Lambda: better support for API-based lambdas (APIGateway)

Parent issue to track features or improvements regarding API-based lambdas.

#### Proposed new features:
* `interactive` mode
* #1840
* Start a server without a payload
* Toolkit attaches a debugger whenever SAM CLI executes a function
* Persist the server until the user closes out the session
* Support more options (port, logging, host, 'warm containers', etc.)
* #2446
* Toolkit may need to explicitly handle these options to work correctly
* A 'workbench' UI for sending payloads to the local API (to pair with `interactive` mode)
* Could either be a notebook or tacked onto the SAM config webview
* More API Gateway resources in templates (e.g. V2)
* #1489
* AWS::Serverless::HttpApi
* "long lived" mode: #2535

#### General improvements and bug fixes:
* Uniform timeouts
* Toolkit currently polls for a set amount of time to wait for the server to start
* Better discoverability
* It's not obvious how to configure things for anything more complex than a 'HelloWorld' project
* Better logging during executions (less noise)
* Fail faster
* Improve the experience by finding common issues with configurations (wrong path, wrong method, etc.)
* Less restrictions on payloads: #2478

This is a parent issue covering interactive execution, server options, a workbench UI, additional API Gateway resources, long-lived mode, logging, timeouts, and payload handling. Start by reviewing the referenced issues (#1840, #2446, #1489, #2535, and #2478) and the SAM config webview mentioned here. There is no single completion condition until one feature is selected and its scope is defined.

Written by the indexing model from the issue text.