Allow ECS Containers to behave like other docker containers in the "vscode-docker" extension

## Problem

The vscode-docker extension that Microsoft provides allows a user to browse the filesystem of a docker container from VSCode.

## Expected behavior

It would be very powerful to be able to perform the same actions with ECS containers.

Start by reading the vscode-docker extension's container-browsing behavior and the toolkit's ECS integration; the issue identifies no repository files or tests. Determine the ECS container operations needed to match the stated filesystem actions, then validate equivalent behavior in VS Code.

Written by the indexing model from the issue text.