TASK 21 slice 2a: native-FPS probe seam (ffprobe parse + derive sibling)

- FfmpegFrameRateParser (pure): prefers avg_frame_rate= then r_frame_rate=,
  rational N/N/M, unknown/0 -> null.
- IFrameRateProbe + FfmpegFrameRateProbe: derives sibling ffprobe.exe from the
  located ffmpeg dir, reuses the IDecodeProcess seam for the ffprobe subprocess
  text; null if ffprobe absent.
- FfmpegLocator now also extracts ffprobe.exe (ProbeFileName) from the pinned
  archive, conditional so old caches without it degrade to no pacing.
- Tests: 6 pure parser units + 1 probe integration via fake locator/process;
  FfmpegLocatorTests still green. 15/15, 0 warnings.

Pacing (probe->delay) is slice 2b. Derivative reference: standard ffprobe
avg_frame_rate probing used across OBS/media tooling.

Services/Encoder/FfmpegLocator.cs

@@ -20,6 +20,11 @@ public sealed class FfmpegLocator : IFfmpegLocator
 {
     public const string FileName = "ffmpeg.exe";
 
+    /// <summary>Sibling probe binary — extracted alongside ffmpeg so the media
+    /// frame-rate probe (<see cref="ytLive.Services.FfmpegFrameRateProbe"/>) can
+    /// derive its path from the located ffmpeg directory.</summary>
+    public const string ProbeFileName = "ffprobe.exe";
+
     /// <summary>Pinned BtbN LGPL-shared win64 build (immutable autobuild tag; see TASKS.md).</summary>
     public const string PinnedUrl =
         "https://github.com/BtbN/FFmpeg-Builds/releases/download/autobuild-2026-08-09-13-03/ffmpeg-master-latest-win64-lgpl-shared.zip";
@@ -85,6 +90,10 @@ public sealed class FfmpegLocator : IFfmpegLocator
                     e => e.FullName.EndsWith("/" + FileName, StringComparison.OrdinalIgnoreCase))
                 ?? throw new InvalidDataException($"The pinned FFmpeg archive does not contain {FileName}.");
             ExtractOne(exe, Path.Combine(staging, FileName));
+            var probe = archive.Entries.FirstOrDefault(
+                e => e.FullName.EndsWith("/" + ProbeFileName, StringComparison.OrdinalIgnoreCase));
+            if (probe != null)
+                ExtractOne(probe, Path.Combine(staging, ProbeFileName));
             foreach (var entry in archive.Entries)
             {
                 if (entry.FullName.EndsWith(".dll", StringComparison.OrdinalIgnoreCase))