Scoop plugin install action crashes when PowerShell script exits with code 1

### Checks

- [x] I have searched the existing issues for duplicates.
- [x] I have included the relevant log excerpt and exception message.

### Problem

Flow Launcher crashed while using the Scoop plugin to install an application from the result context menu.

### Environment

- Flow Launcher version: 2.1.3
- OS Version: 22621.3447
- IntPtr Length: 8
- x64: True
- Python Path: `E:\scoop\apps\python\current\pythonw.exe`
- Node Path: `D:\IT\node\node.exe`
- Date: `09/12/2026 14:56:16`
- Scoop installation detected by Flow Launcher: `User: root=E:\scoop, apps=E:\scoop\apps; administrator=False`
- Scoop plugin assembly: `Flow.Launcher.Plugin.Scoop, Version=1.0.0.0`
- Installed Scoop plugin path shown in log: `E:\scoop\apps\Flow-Launcher\current\app-2.1.3\UserData\Plugins\Scoop-1.0.2\Flow.Launcher.Plugin.Scoop.dll`

### What happened

When selecting the Scoop install action, Flow Launcher reported an unhandled exception because `powershell.exe` script execution failed with exit code `1`. The exception does not include the underlying PowerShell error output, so the UI/log only shows an empty `Error Output:` value.

### Relevant log excerpt

Log file on my machine:

`E:\scoop\apps\Flow-Launcher\current\app-2.1.3\UserData\Logs\2.1.3\Flow.Launcher.2026-09-12.log`

```text
14:54:26.9170+08:00 - INFO - SearchHelper.LogInfo - Built Scoop search index: buckets=10, manifestFiles=5939, entries=5939, cacheHits=0, persistentHits=0, filesRead=5939, parsed=5939, invalid=0, readFailures=0, parseFailures=0, fileStampFailures=0, persistentWrite=False, elapsedMs=1611.
14:54:27.1534+08:00 - INFO - SearchHelper.LogInfo - Built Scoop search index: buckets=10, manifestFiles=5939, entries=5939, cacheHits=5939, persistentHits=0, filesRead=0, parsed=0, invalid=0, readFailures=0, parseFailures=0, fileStampFailures=0, persistentWrite=False, elapsedMs=236.
14:55:46.9874+08:00 - INFO - SearchHelper.LogInfo - Built Scoop search index: buckets=10, manifestFiles=5946, entries=5946, cacheHits=5416, persistentHits=0, filesRead=530, parsed=530, invalid=0, readFailures=0, parseFailures=0, fileStampFailures=0, persistentWrite=False, elapsedMs=268.
14:56:15.7572+08:00 - FATAL - DispatcherUnhandledException -
## Exception

System.Exception: powershell.exe script execution failed. Exit code: 1. Error Output:
Source: Flow.Launcher.Plugin.Scoop
TargetAssembly: Flow.Launcher.Plugin.Scoop, Version=1.0.0.0, Culture=neutral, PublicKeyToken=null
TargetModule: Flow.Launcher.Plugin.Scoop.dll
TargetSite: Void MoveNext()
at Flow.Launcher.Plugin.Scoop.Helper.ScoopPwshExecutor.ExecuteCommandWithShellAsync(String shellExecutable, String command, CancellationToken cancellationToken)
at Flow.Launcher.Plugin.Scoop.Helper.ScoopPwshExecutor.ExecuteCommandWithOutputAsync(String command, CancellationToken cancellationToken)
at Flow.Launcher.Plugin.Scoop.Helper.ScoopPwshExecutor.ExecuteCommandAsync(String command)
at Flow.Launcher.Plugin.Scoop.Helper.ScoopPwshExecutor.ExecuteOperationAsync(String command, String title, String subTitle, String successMessage, String errorTitle, PluginInitContext context, Boolean requiresAdministrator)
at Flow.Launcher.Plugin.Scoop.Entity.ContextMenu.<>c__DisplayClass5_0.<b__1>d.MoveNext()
--- End of stack trace from previous location ---
at Flow.Launcher.ViewModel.MainViewModel.OpenResultAsync(String index) in C:\projects\flow-launcher\Flow.Launcher\ViewModel\MainViewModel.cs:line 520
at CommunityToolkit.Mvvm.Input.AsyncRelayCommand.AwaitAndThrowIfFailed(Task executionTask)
at System.Threading.Tasks.Task.<>c.b__128_0(Object state)
at System.Windows.Threading.ExceptionWrapper.InternalRealCall(Delegate callback, Object args, Int32 numArgs)
at System.Windows.Threading.ExceptionWrapper.TryCatchWhen(Object source, Delegate callback, Object args, Int32 numArgs, Delegate catchHandler)
```

### Exception message copied from Flow Launcher

```text
Flow Launcher version: 2.1.3
OS Version: 22621.3447
IntPtr Length: 8
x64: True

Python Path: E:\scoop\apps\python\current\pythonw.exe
Node Path: D:\IT\node\node.exe

Date: 09/12/2026 14:56:16
Exception:
System.Exception: powershell.exe script execution failed. Exit code: 1. Error Output:
at Flow.Launcher.Plugin.Scoop.Helper.ScoopPwshExecutor.ExecuteCommandWithShellAsync(String shellExecutable, String command, CancellationToken cancellationToken)
at Flow.Launcher.Plugin.Scoop.Helper.ScoopPwshExecutor.ExecuteCommandWithOutputAsync(String command, CancellationToken cancellationToken)
at Flow.Launcher.Plugin.Scoop.Helper.ScoopPwshExecutor.ExecuteCommandAsync(String command)
at Flow.Launcher.Plugin.Scoop.Helper.ScoopPwshExecutor.ExecuteOperationAsync(String command, String title, String subTitle, String successMessage, String errorTitle, PluginInitContext context, Boolean requiresAdministrator)
at Flow.Launcher.Plugin.Scoop.Entity.ContextMenu.<>c__DisplayClass5_0.<b__1>d.MoveNext()
--- End of stack trace from previous location ---
at Flow.Launcher.ViewModel.MainViewModel.OpenResultAsync(String index) in C:\projects\flow-launcher\Flow.Launcher\ViewModel\MainViewModel.cs:line 520
at CommunityToolkit.Mvvm.Input.AsyncRelayCommand.AwaitAndThrowIfFailed(Task executionTask)
at System.Threading.Tasks.Task.<>c.b__128_0(Object state)
at System.Windows.Threading.ExceptionWrapper.InternalRealCall(Delegate callback, Object args, Int32 numArgs)
at System.Windows.Threading.ExceptionWrapper.TryCatchWhen(Object source, Delegate callback, Object args, Int32 numArgs, Delegate catchHandler)
```

### Additional note

The full local log file is about 162 KB. I can provide/upload it if needed; the most relevant crash section is included above.

Start in Flow.Launcher.Plugin.Scoop.Helper.ScoopPwshExecutor, following ExecuteCommandWithShellAsync through ExecuteCommandWithOutputAsync and ExecuteOperationAsync; the stack trace identifies these entry points. Reproduce the Scoop install failure and verify that the resulting error includes the PowerShell output instead of an empty Error Output and an unhandled crash.

Written by the indexing model from the issue text.