总结如下：

• 您的问题是，您希望计划任务使用的模块安装在 * 当前用户 * 的范围内，而以 * 不同 * 用户身份运行的任务（如NT AUTORITY\SYSTEM）将 * 看不到 * 该模块。
• 最简单的解决方案是通过将-Scope AllUsers参数传递给Install-Module（需要提升），为 * 所有 * 用户安装该模块。
• 然而，即使这是"不"可能或不希望的，也有一个解决方案，即将"完整模块路径"传递给在任务上下文中执行的显式Import-Module调用，如下所示。
• 由于您的任务需要在提升的情况下运行，如您所述，只有当用户是管理员时，才可以选择在 * current * 用户的上下文中运行;正如您所发现的，您可以按如下方式进行设置（需要高程）：

$taskPrincipal = 
  New-ScheduledTaskPrincipal -LogonType S4U -UserId $env:USERNAME -RunLevel Highest

• 以用户NT AUTORITY\SYSTEM的身份运行任务 * 总是 * 运行：
• 假定该帐户是具有广泛的 * 本地 * 特权的高特权内置帐户，并且其"充当网络上的计算机"，则使用提升。
• 不可见地（在服务运行的同一隐藏会话/窗口站中，因此使用-LogonType Service。
• 用户当前是否已登录
• 默认情况下C:\Windows\System32为工作控制器
• 值<hostname>$反映在$env:USERNAME中，其中<hostname>是本地计算机的名称，以及C:\Windows\system32\config\systemprofile的$HOME/$env:USERPROFILE文件夹。

以下自包含示例：

• 创建任务，该任务在创建后5秒执行 * 一次 *
• 以NT AUTHORITY\SYSTEM运行
• 在当前用户的主目录中创建任务明确导入的示例脚本模块
• 从该模块调用函数，该函数报告有关运行时环境的信息，并将结果记录在当前用户主目录的文本文件中。
• 等待任务运行并显示记录的信息。
• 清除后自己（创建的临时文件为~/_test.psm1和~/_test.txt，临时任务命名为_Test）

#requires -RunAsAdministrator

# Abort on any error.
# Note: Since the *-ScheduledTask* cmdlets are implemented as 
#       CDXML-based *script* modules, they only see preference vars.
#       in the *global* scope - see https://github.com/PowerShell/PowerShell/issues/4568
$prevEaPref = $global:ErrorActionPreference
$global:ErrorActionPreference = 'Stop'

try {

    # Create a simple script module that exports function Get-Foo,
    # in the current user's home dir., named '_test.psm1'
    @'
function Get-Foo { "Hi, I'm running at $(Get-Date)`n * as $env:USERNAME (whose home dir. is '$HOME')`n * in '$PWD'`n * $(('NON-elevated', 'ELEVATED')[[bool] (net session 2>$null)])." }
'@ > ~/_test.psm1

    # Set up the scheduled task:

    # The command (program) to run.
    # Import the test-module via its full path, call Get-Foo, and redirect all output streams
    # to file '_test.txt' in the current users' home dir.
    $action = New-ScheduledTaskAction -Execute powershell -Argument "-ExecutionPolicy Bypass -NoProfile -Command & { Import-Module `"$((Get-Item ~/_test.psm1).FullName)`"; Get-Foo } *> `"$((Get-Item ~).FullName)\_test.txt`""

    # Run as 'NT AUTHORITY\SYSTEM', which runs:
    #  * invisibly
    #  * whether or not someone is logged on
    #  * implicitly with elevation
    $user = New-ScheduledTaskPrincipal -UserID 'NT AUTHORITY\SYSTEM' -LogonType ServiceAccount

    # # Advanced settings such as whether to allow start on demand, not running when on batter power, ... 
    # $settings = New-ScheduledTaskSettingsSet

    # When to run it: Run a few seconds from now, once.
    $secsFromNow = 5
    $when = (Get-Date).AddSeconds($secsFromNow)
    $trigger = New-ScheduledTaskTrigger -Once -At $when

    # Create the task from the above.
    $newTask = New-ScheduledTask -Action $action -Principal $user -Trigger $trigger

    # Register the task with name '_Test'
    Write-Verbose -Verbose "Creating task..."
    Register-ScheduledTask '_Test' -InputObject $newTask -Force

    Write-Verbose -Verbose "Task will execute invisibly in $secsFromNow seconds, running as 'NT AUTHORITY\SYSTEM'. Waiting (plus a few extra seconds)..."
    Start-Sleep ($secsFromNow + 5) # Wait an extra few seconds to give the task time to complete.

    Write-Verbose -Verbose "Task is assumed to have run. Output logged:"
    Get-Content ~/_test.txt
}
finally {
    # Clean up.
    Remove-Item -ErrorAction Ignore ~/_test.psm1, ~/_test.txt
    Unregister-ScheduledTask -ErrorAction Ignore -TaskName _Test -Confirm:$false
    $global:ErrorActionPreference = $prevEaPref
}

样本输出：

VERBOSE: Creating task...

TaskPath                                       TaskName                          State
--------                                       --------                          -----
\                                              _Test                             Ready
VERBOSE: Task will execute invisibly in 5 seconds, running as 'NT AUTHORITY\SYSTEM'. Waiting (plus a few extra seconds)...
VERBOSE: Task is assumed to have run. Output logged:
Hi, I'm running at 01/11/2023 17:06:04
 * as WORKSTATION1$ (whose home dir. is 'C:\Windows\system32\config\systemprofile')
 * in 'C:\Windows\system32'
 * ELEVATED.

最后4行是模块函数（Get-Foo）的输出，证明模块已成功导入到任务上下文中。