Changing culture settings is not taken into account in the PowerShell Extension's PowerShell instance

Prerequisites

• I have written a descriptive issue title.
• I have searched all open and closed 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

Changing the culture's settings such as the time format has no effect in the PowerShell Extension:

PowerShell Version

PSVersion                      7.3.7
PSEdition                      Core
GitCommitId                    7.3.7
OS                             Microsoft Windows 10.0.22621
Platform                       Win32NT
PSCompatibleVersions           {1.0, 2.0, 3.0, 4.0…}
PSRemotingProtocolVersion      2.3
SerializationVersion           1.1.0.1
WSManStackVersion              3.0

Visual Studio Code Version

1.82.2
abd2f3db4bdb28f9e95536dfa84d8479f1eb312d
x64

Extension Version

ms-vscode.powershell@2023.9.4
TylerLeonhardt.vscode-inline-values-powershell@0.0.7

Steps to Reproduce

From the PowerShell Extension's PowerShell prompt, run the following script:

    # derived from https://github.com/PowerShell/PowerShell/issues/19536#issuecomment-1515140128
    # Save the original culture.
    $global:originalculture = [cultureinfo]::CurrentCulture

    # Temporarily replace it with a read/write copy.
    [cultureinfo]::CurrentCulture = [cultureinfo] $global:originalculture.Name


    # Modify the LongTimePattern format to include milliseconds.
    [cultureinfo]::CurrentCulture.DateTimeFormat.LongTimePattern += ([cultureinfo]::CurrentCulture.NumberFormat.CurrencyDecimalSeparator + 'fff')

This has no effect to e.g. the output from Get-Date:

PS> Set-LongTimePatternToIncludeMilliseconds.ps1
PS> Get-Date

Saturday, September 30, 2023 12:23:05

Whereas the result is correct in a "normal" PowerShell instance:

PS> Set-LongTimePatternToIncludeMilliseconds.ps1
PS> get-date

Saturday, September 30, 2023 12:24:17.297

Visuals

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Logs

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