feat(ui): add current-launch logs tab

Add Live Chat and Logs tabs to the non-edit left panel. Expose a bounded process-local AppLog feed so the newest messages appear first without importing earlier startup.log contents or changing file logging.

Ref: https://obsproject.com/forum/resources/understanding-obs-studio-log.473

Helpers/AppLog.cs

@@ -12,6 +12,7 @@ public static class AppLog
 {
     /// <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;
+    private const int CurrentLaunchEntryLimit = 500;
 
     /// <summary>How many rolled copies to keep (startup.1.log, startup.2.log, …).</summary>
     private const int RetainedFiles = 1;
@@ -20,6 +21,8 @@ public static class AppLog
         InstanceProfile.DataRoot, "startup.log");
 
     private static readonly object Gate = new();
+    private static readonly List<AppLogEntry> CurrentLaunchEntries = new();
+    private static long _nextSequence;
 
     /// <summary>Test seam: point the log somewhere else. Null = the real profile's log.</summary>
     internal static string? PathOverride { get; set; }
@@ -29,16 +32,29 @@ public static class AppLog
 
     private static string LogPath => PathOverride ?? DefaultLogPath;
 
+    internal static IReadOnlyList<AppLogEntry> SnapshotCurrentLaunch()
+    {
+        lock (Gate)
+            return CurrentLaunchEntries.ToArray();
+    }
+
     public static void Write(string message)
     {
         try
         {
             lock (Gate)
             {
+                var entry = new AppLogEntry(
+                    ++_nextSequence,
+                    $"{DateTime.Now:yyyy-MM-dd HH:mm:ss.fff} {message}");
+                CurrentLaunchEntries.Add(entry);
+                if (CurrentLaunchEntries.Count > CurrentLaunchEntryLimit)
+                    CurrentLaunchEntries.RemoveAt(0);
+
                 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}");
+                File.AppendAllText(path, $"{entry.Text}{Environment.NewLine}");
             }
         }
         catch
@@ -52,3 +68,5 @@ public static class AppLog
         Write($"{message}: {exception}");
     }
 }
+
+public sealed record AppLogEntry(long Sequence, string Text);