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/index.md

@@ -6,7 +6,7 @@ Cross-cutting utilities. See [`schema.md`](../schema.md) for the memory-map conv
 |------|---------|
 | `ViewModelBase.cs` | `INotifyPropertyChanged` + `SetProperty<T>()` — base for all ViewModels |
 | `RelayCommand.cs` | `ICommand` implementation for all button actions |
-| `AppLog.cs` | File logger to `%APPDATA%\ytLlive\startup.log`; startup checkpoints + unhandled-exception capture (the crash this map is named for). Size-capped: rolls to `startup.1.log` at 5 MB (TASK 55) |
+| `AppLog.cs` | File logger to `%APPDATA%\ytLlive\startup.log`; startup checkpoints + unhandled-exception capture. Size-capped: rolls to `startup.1.log` at 5 MB (TASK 55). Also keeps the newest 500 formatted entries in a process-local buffer for the Logs tab; it never loads prior-launch file contents |
 | `LogRotation.cs` | The size-capped-rotation policy as a pure function over a path: roll `startup.log` → `startup.1.log` when it passes the cap, keeping N rolled copies. Separate from `AppLog` so the logger's 156-call-site surface never changes and the rule is testable alone (TASK 55) |
 | `FocusPreservingListBox.cs` | `ListBox` subclass that keeps selection/focus coherent when the selected item is deleted; `IsSelectable` predicate skips hidden scenes; drag-reorder guard |
 | `OAuthCredentials.cs` | Baked-in Google OAuth client ID/secret (desktop app; loopback callback) |