TASK 55 slice 1: the startup log is size-capped

The creator (2026-10-09): 'we need some sort of log-rotation so that we don't
inadvertently fill up a user's drive.' startup.log was uncapped - 23MB and growing
every few seconds, because FfmpegEncoder logs every non-progress ffmpeg stderr line.

The policy lives in a new Helpers/LogRotation.cs as a pure function over a path
(RollIfNeeded(logPath, maxBytes, retainedFiles)), so AppLog's 156 call sites keep
their surface and the rule is testable on its own. At 5MB the live file rolls to
startup.1.log and one rolled copy is kept - the FILE SET is bounded, not just the
live file, so a long stream cannot grow the log without limit. A failed rotation
degrades to the old behaviour instead of taking the app down.

Pattern reference (cited): Serilog's file sink pairs fileSizeLimitBytes (the cap)
with retainedFileCountLimit (how many rolled files to keep) -
https://github.com/serilog/serilog-sinks-file

Guard: ytLive.Tests/AppLogRotationTests.cs - the ONE test drives the real
AppLog.Write against a temp dir (two internal seams: PathOverride, MaxBytes) and
asserts the roll, the fresh live file, and that after a SECOND roll the directory
still holds exactly startup.log + startup.1.log.

Also fixed a stale catalog row: TASK 12 (master limiter) shipped 2026-08-15 and was
still marked 'Queued'.

Helpers/AppLog.cs

@@ -10,19 +10,35 @@ namespace ytLive.Helpers;
 /// </summary>
 public static class AppLog
 {
-    private static readonly string LogPath = Path.Combine(
+    /// <summary>The cap for the live log file. Past this, it rolls to <c>startup.1.log</c>.</summary>
+    private const long DefaultMaxBytes = 5 * 1024 * 1024;
+
+    /// <summary>How many rolled copies to keep (startup.1.log, startup.2.log, …).</summary>
+    private const int RetainedFiles = 1;
+
+    private static readonly string DefaultLogPath = Path.Combine(
         InstanceProfile.DataRoot, "startup.log");
 
     private static readonly object Gate = new();
 
+    /// <summary>Test seam: point the log somewhere else. Null = the real profile's log.</summary>
+    internal static string? PathOverride { get; set; }
+
+    /// <summary>Test seam: the cap that triggers a roll.</summary>
+    internal static long MaxBytes { get; set; } = DefaultMaxBytes;
+
+    private static string LogPath => PathOverride ?? DefaultLogPath;
+
     public static void Write(string message)
     {
         try
         {
             lock (Gate)
             {
-                Directory.CreateDirectory(Path.GetDirectoryName(LogPath)!);
-                File.AppendAllText(LogPath, $"{DateTime.Now:yyyy-MM-dd HH:mm:ss.fff} {message}{Environment.NewLine}");
+                var path = LogPath;
+                Directory.CreateDirectory(Path.GetDirectoryName(path)!);
+                LogRotation.RollIfNeeded(path, MaxBytes, RetainedFiles);
+                File.AppendAllText(path, $"{DateTime.Now:yyyy-MM-dd HH:mm:ss.fff} {message}{Environment.NewLine}");
             }
         }
         catch