feat(daily-prep): persist last prep run to a log file and serve it via GetLastPrepLog

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

src/ClaudeDo.Worker/Prime/PrimeRunner.cs

@@ -39,6 +39,10 @@ public sealed class PrimeRunner : IPrimeRunner
         var success = false;
         try
         {
+            var logPath = DailyPrepPrompt.LogPath();
+            try { if (File.Exists(logPath)) File.Delete(logPath); } catch { /* best effort */ }
+            await using var logWriter = new LogWriter(logPath);
+
             await _broadcaster.PrepStartedAsync();
 
             var cwd = Paths.AppDataRoot();
@@ -62,7 +66,11 @@ public sealed class PrimeRunner : IPrimeRunner
                 arguments: args,
                 prompt: prompt,
                 workingDirectory: cwd,
-                onStdoutLine: line => _broadcaster.PrepLineAsync(line),
+                onStdoutLine: async line =>
+                {
+                    await logWriter.WriteLineAsync(line);
+                    await _broadcaster.PrepLineAsync(line);
+                },
                 ct: timeoutCts.Token);
 
             success = result.IsSuccess;