Clear of console and content vanishing after resize

Prerequisites

• I have written a descriptive issue title.
• I have searched all issues to ensure it has not already been reported.
• I have read the troubleshooting guide.
• I am sure this issue is with the extension itself and does not reproduce in a standalone PowerShell instance.
• I have verified that I am using the latest version of Visual Studio Code and the PowerShell extension.
• If this is a security issue, I have read the security issue reporting guidance.

Summary

As discussed on Discord -> Problems with resize, write-progress:

Clear-Host not working properly

Is enabled:

    "terminal.integrated.windowsEnableConpty": true,

PowerShell Version

Name                           Value
----                           -----
PSVersion                      5.1.22000.652
PSEdition                      Desktop
PSCompatibleVersions           {1.0, 2.0, 3.0, 4.0...}
BuildVersion                   10.0.22000.652
CLRVersion                     4.0.30319.42000
WSManStackVersion              3.0
PSRemotingProtocolVersion      2.3
SerializationVersion           1.1.0.1

Visual Studio Code Version

1.67.1
da15b6fd3ef856477bf6f4fb29ba1b7af717770d
x64

Extension Version

ms-vscode.powershell@2022.5.1
ms-vscode.powershell-preview@2022.5.1
tobysmith568.run-in-powershell@1.1.1
TylerLeonhardt.vscode-inline-values-powershell@0.0.5

Steps to Reproduce

As shown on GIFs try to do something in the console, resize, console up and down, type again, and notice how things get distorted.

Visuals

No response

Logs

No response

Start by reproducing the console resize and Clear-Host behavior shown in the linked GIFs, using the reported PowerShell 5.1, VS Code 1.67.1, and extension 2022.5.1 versions with ConPTY enabled. The payload names no source files or tests, so tracing the extension's terminal handling will be necessary; done means resizing, clearing, and typing no longer distort or lose console content.