BUG: crashed while tring to use search plug in

### Checks

- [ ] I have checked that this issue has not already been reported.

- [x] I am using the latest version of Flow Launcher.

- [ ] I am using the prerelease version of Flow Launcher.

### Problem Description

Flow Launcher version: 2.0.3
OS Version: 26200.7623
IntPtr Length: 8
x64: True

Python Path: C:\Users\bayzed\AppData\Roaming\FlowLauncher\Environments\Python\PythonEmbeddable-v3.11.4\pythonw.exe
Node Path:

Date: 02/08/2026 20:01:08
Exception:
System.UriFormatException: Invalid URI: The format of the URI could not be determined.
at System.Uri.CreateThis(String uri, Boolean dontEscape, UriKind uriKind, UriCreationOptions& creationOptions)
at System.Uri..ctor(String uriString)
at Flow.Launcher.PublicAPIInstance.OpenWebUrl(String url, Nullable`1 inPrivate) in C:\projects\flow-launcher\Flow.Launcher\PublicAPIInstance.cs:line 467
at Flow.Launcher.Plugin.WebSearch.Main.<>c__DisplayClass9_1.b__1(ActionContext c) in C:\projects\flow-launcher\Plugins\Flow.Launcher.Plugin.WebSearch\Main.cs:line 74
at Flow.Launcher.Plugin.Result.ExecuteAsync(ActionContext context) in /_/Flow.Launcher.Plugin/Result.cs:line 281
at Flow.Launcher.ViewModel.MainViewModel.OpenResultAsync(String index) in C:\projects\flow-launcher\Flow.Launcher\ViewModel\MainViewModel.cs:line 518
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)

### To Reproduce

1. ...
2. ...
3. ...

### Screenshots

_No response_

### Flow Launcher Version

Flow Launcher version: 2.0.3

### Windows Build Number

OS Version: 26200.7623

### Error Log

```shell

Replace this line with the important log contents.

```

Start with Flow.Launcher/PublicAPIInstance.cs at line 467 and the WebSearch entry point in Plugins/Flow.Launcher.Plugin.WebSearch/Main.cs at line 74, following the reported UriFormatException. Reproduce the crash while using the search plugin and determine which input triggers it. Done means the same search action no longer crashes and the reported invalid URI condition is handled.

Written by the indexing model from the issue text.