Poor experience when using EC2 connect feature on OSX

## Problem

## Steps to reproduce the issue

1. Connect a session to an EC2 instance
2. Let screen lock on OSX or otherwise time out the EC2 connect session
3. Clicking on VSCode now prompts with 'Disconnected. Attempting to reconnect...'
4. VSCode prompts with 'Cannot reconnect. Please reload the window.'
5. Selecting 'Reload' prompts with error box 'Failed to connect to the remote extension host server (Error: The connection timed out)'

The only way to re-access the session is to then close the window, and reconnect.

This also leaves a dangling session-manager-plugin ( /Users/nbaws/Library/Application Support/Code/User/globalStorage/amazonwebservices.aws-toolkit-vscode/tools/Amazon/sessionmanagerplugin/bin/session-manager-plugin ), which can result in many of these plugin processes dangling over time.

## Expected behavior

The failed connection is detected, connection is re-established cleanly, either using a new session-manager-plugin instance or reusing the existing one.

## System details (run `AWS: About` and/or `Amazon Q: About`)

OS: Darwin arm64 24.4.0
Visual Studio Code extension host: 1.99.3
AWS Toolkit: 3.55.0
node: 20.18.3
electron: 34.3.2

Start by reproducing the EC2 Connect session timeout on macOS with the listed VS Code and AWS Toolkit versions, then inspect the connection flow around session-manager-plugin. Verify the failure after screen lock and determine how reconnection is currently handled. Done means the session reconnects cleanly after timeout and no dangling session-manager-plugin process remains.

Written by the indexing model from the issue text.