fix(worker): resolve claude CLI shims (.cmd/.bat) not just .exe on PATH

UseShellExecute=false only appends .exe when searching PATH, so an
npm-installed claude.cmd was never found even though it works from a shell.
Adds a shared ExecutableResolver in ClaudeDo.Data (PATH/PATHEXT aware, with
known npm/claude install-dir fallbacks) and wires it into ClaudeCliPreflight
and ClaudeProcess; shims are launched via cmd.exe /c.

src/ClaudeDo.Data/Environment/ExecutableResolver.cs

@@ -0,0 +1,112 @@
+using SysEnvironment = System.Environment;
+
+namespace ClaudeDo.Data.Environment;
+
+public sealed record ResolvedExecutable(string Path, bool IsShim);
+
+public sealed record ShimStartInfo(string FileName, string Arguments);
+
+/// <summary>
+/// Resolves a command the way Windows' CreateProcess/PATH search does, but also finds
+/// non-.exe shims (.cmd/.bat/.ps1) that UseShellExecute=false alone would miss.
+/// </summary>
+public static class ExecutableResolver
+{
+    private const string DefaultPathExt = ".COM;.EXE;.BAT;.CMD";
+
+    // Known npm/claude install locations to try when PATH search comes up empty.
+    private static readonly string[] FallbackDirectoryTemplates =
+    {
+        "%APPDATA%\\npm",
+        "%LOCALAPPDATA%\\Programs\\claude",
+        "%USERPROFILE%\\.local\\bin",
+    };
+
+    public static ResolvedExecutable? Resolve(string command, string? pathOverride = null, string? pathExtOverride = null)
+    {
+        var pathExts = ParsePathExt(pathExtOverride);
+
+        if (LooksLikePath(command))
+        {
+            return ResolveAsPath(command, pathExts);
+        }
+
+        var directories = ParsePath(pathOverride);
+        foreach (var dir in directories)
+        {
+            var resolved = ResolveInDirectory(dir, command, pathExts);
+            if (resolved is not null) return resolved;
+        }
+
+        foreach (var template in FallbackDirectoryTemplates)
+        {
+            var dir = SysEnvironment.ExpandEnvironmentVariables(template);
+            var resolved = ResolveInDirectory(dir, command, pathExts);
+            if (resolved is not null) return resolved;
+        }
+
+        return null;
+    }
+
+    public static ShimStartInfo BuildShimStartInfo(string shimPath, IReadOnlyList<string> arguments)
+    {
+        var parts = new List<string> { "/c", Quote(shimPath) };
+        parts.AddRange(arguments.Select(Quote));
+        return new ShimStartInfo("cmd.exe", string.Join(' ', parts));
+    }
+
+    private static bool LooksLikePath(string command) =>
+        command.Contains(Path.DirectorySeparatorChar) || command.Contains(Path.AltDirectorySeparatorChar);
+
+    private static ResolvedExecutable? ResolveAsPath(string command, IReadOnlyList<string> pathExts)
+    {
+        if (File.Exists(command)) return new ResolvedExecutable(command, IsShimExtension(Path.GetExtension(command)));
+
+        if (Path.HasExtension(command)) return null;
+
+        foreach (var ext in pathExts)
+        {
+            var candidate = command + ext;
+            if (File.Exists(candidate)) return new ResolvedExecutable(candidate, IsShimExtension(ext));
+        }
+
+        return null;
+    }
+
+    private static ResolvedExecutable? ResolveInDirectory(string directory, string command, IReadOnlyList<string> pathExts)
+    {
+        if (!Directory.Exists(directory)) return null;
+
+        if (Path.HasExtension(command))
+        {
+            var candidate = Path.Combine(directory, command);
+            return File.Exists(candidate) ? new ResolvedExecutable(candidate, IsShimExtension(Path.GetExtension(candidate))) : null;
+        }
+
+        foreach (var ext in pathExts)
+        {
+            var candidate = Path.Combine(directory, command + ext);
+            if (File.Exists(candidate)) return new ResolvedExecutable(candidate, IsShimExtension(ext));
+        }
+
+        return null;
+    }
+
+    private static bool IsShimExtension(string extension) =>
+        !extension.Equals(".exe", StringComparison.OrdinalIgnoreCase)
+        && !extension.Equals(".com", StringComparison.OrdinalIgnoreCase);
+
+    private static IReadOnlyList<string> ParsePathExt(string? pathExtOverride)
+    {
+        var raw = pathExtOverride ?? SysEnvironment.GetEnvironmentVariable("PATHEXT") ?? DefaultPathExt;
+        return raw.Split(';', StringSplitOptions.RemoveEmptyEntries | StringSplitOptions.TrimEntries);
+    }
+
+    private static IReadOnlyList<string> ParsePath(string? pathOverride)
+    {
+        var raw = pathOverride ?? SysEnvironment.GetEnvironmentVariable("PATH") ?? "";
+        return raw.Split(Path.PathSeparator, StringSplitOptions.RemoveEmptyEntries | StringSplitOptions.TrimEntries);
+    }
+
+    private static string Quote(string value) => value.Contains(' ') ? $"\"{value}\"" : value;
+}

src/ClaudeDo.Data/Paths.cs

@@ -11,16 +11,16 @@ public static class Paths
         if (string.IsNullOrWhiteSpace(path))
             throw new ArgumentException("Path must not be empty.", nameof(path));
 
-        var expanded = Environment.ExpandEnvironmentVariables(path);
+        var expanded = System.Environment.ExpandEnvironmentVariables(path);
 
         if (expanded.StartsWith("~", StringComparison.Ordinal))
         {
-            var home = Environment.GetFolderPath(Environment.SpecialFolder.UserProfile);
+            var home = System.Environment.GetFolderPath(System.Environment.SpecialFolder.UserProfile);
             expanded = home + expanded[1..];
         }
 
         if (!Path.IsPathRooted(expanded))
-            expanded = Path.GetFullPath(expanded, baseDir ?? Environment.CurrentDirectory);
+            expanded = Path.GetFullPath(expanded, baseDir ?? System.Environment.CurrentDirectory);
 
         return Path.GetFullPath(expanded);
     }