BUG: Failed to init Browser Bookmark search plugin

### Checks

- [x] 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

When I start Flow Launcher, I get a system notification that the Browser Bookmarks plugin failed to load.

I only installed today, so I am assuming that #4491 is ***NOT*** a duplicate.

### To Reproduce

1. Start or restart Flow Launcher

### Screenshots

### Flow Launcher Version

2.1.3

### Windows Build Number

10.0.26200.8737

### Error Log

```shell

10:45:31.6604+01:00 - ERROR - PluginManager.InitializePluginsAsync - Fail to Init plugin: Browser Bookmarks
EXCEPTION OCCURS: System.UnauthorizedAccessException: Access to the path 'C:\Users\Paul\AppData\Local\Google\Chrome\User Data\Default\Bookmarks' is denied.
at SafeFileHandle Microsoft.Win32.SafeHandles.SafeFileHandle.CreateFile(string fullPath, FileMode mode, FileAccess access, FileShare share, FileOptions options)
at SafeFileHandle Microsoft.Win32.SafeHandles.SafeFileHandle.Open(string fullPath, FileMode mode, FileAccess access, FileShare share, FileOptions options, long preallocationSize, UnixFileMode? unixCreateMode)
at new System.IO.Strategies.OSFileStreamStrategy(string path, FileMode mode, FileAccess access, FileShare share, FileOptions options, long preallocationSize, UnixFileMode? unixCreateMode)
at FileStreamStrategy System.IO.Strategies.FileStreamHelpers.ChooseStrategyCore(string path, FileMode mode, FileAccess access, FileShare share, FileOptions options, long preallocationSize, UnixFileMode? unixCreateMode)
at FileStream System.IO.StreamReader.ValidateArgsAndOpenPath(string path, Encoding encoding, int bufferSize)
at string System.IO.File.ReadAllText(string path, Encoding encoding)
at List Flow.Launcher.Plugin.BrowserBookmark.ChromiumBookmarkLoader.LoadBookmarksFromFile(string path, string source) in C:/projects/flow-launcher/Plugins/Flow.Launcher.Plugin.BrowserBookmark/ChromiumBookmarkLoader.cs:line 81
at List Flow.Launcher.Plugin.BrowserBookmark.ChromiumBookmarkLoader.LoadBookmarks(string browserDataPath, string name) in C:/projects/flow-launcher/Plugins/Flow.Launcher.Plugin.BrowserBookmark/ChromiumBookmarkLoader.cs:line 53
at List Flow.Launcher.Plugin.BrowserBookmark.ChromeBookmarkLoader.LoadChromeBookmarks() in C:/projects/flow-launcher/Plugins/Flow.Launcher.Plugin.BrowserBookmark/ChromeBookmarkLoader.cs:line 18
at List Flow.Launcher.Plugin.BrowserBookmark.ChromeBookmarkLoader.GetBookmarks() in C:/projects/flow-launcher/Plugins/Flow.Launcher.Plugin.BrowserBookmark/ChromeBookmarkLoader.cs:line 12
at List Flow.Launcher.Plugin.BrowserBookmark.Commands.BookmarkLoader.LoadAllBookmarks(Settings setting) in C:/projects/flow-launcher/Plugins/Flow.Launcher.Plugin.BrowserBookmark/Commands/BookmarkLoader.cs:line 27
at void Flow.Launcher.Plugin.BrowserBookmark.Main.LoadBookmarksIfEnabled() in C:/projects/flow-launcher/Plugins/Flow.Launcher.Plugin.BrowserBookmark/Main.cs:line 74
at void Flow.Launcher.Plugin.BrowserBookmark.Main.Init(PluginInitContext context) in C:/projects/flow-launcher/Plugins/Flow.Launcher.Plugin.BrowserBookmark/Main.cs:line 60
at Task Flow.Launcher.Plugin.IPlugin.Flow.Launcher.Plugin.IAsyncPlugin.InitAsync(PluginInitContext context)+() => { } in /_/Flow.Launcher.Plugin/Interfaces/IPlugin.cs:line 33
at async Task Flow.Launcher.Infrastructure.Stopwatch.DebugAsync(string className, string message, Func action, string methodName) in C:/projects/flow-launcher/Flow.Launcher.Infrastructure/Stopwatch.cs:line 31
at async Task Flow.Launcher.Core.Plugin.PluginManager.InitializePluginsAsync(IResultUpdateRegister register)+(?) => { } in C:/projects/flow-launcher/Flow.Launcher.Core/Plugin/PluginManager.cs:line 266
```

Start with Plugins/Flow.Launcher.Plugin.BrowserBookmark/ChromiumBookmarkLoader.cs at line 81, then follow the initialization path through BookmarkLoader.cs and Main.cs. Reproduce by starting Flow Launcher with the reported Chrome profile and inspect how the access-denied error propagates. Done should address the Browser Bookmarks plugin failing to initialize in this situation without obscuring unrelated errors.

Written by the indexing model from the issue text.