MediaCapture: Add FFmpeg backend

scripts/flatpak/org.duckstation.DuckStation.yaml

@@ -4,6 +4,12 @@ runtime-version: "6.7"
 sdk: "org.kde.Sdk"
 sdk-extensions:
   - "org.freedesktop.Sdk.Extension.llvm17"
+add-extensions:
+  "org.freedesktop.Platform.ffmpeg-full":
+    directory: "lib/ffmpeg"
+    version: "23.08"
+    add-ld-path: "."
+    autodownload: true
 
 command: "duckstation-qt"
 
@@ -80,3 +86,6 @@ modules:
         install -Dm644
         "${FLATPAK_BUILDER_BUILDDIR}/scripts/flatpak/org.duckstation.DuckStation.metainfo.xml"
         "${FLATPAK_DEST}/share/metainfo/org.duckstation.DuckStation.metainfo.xml"
+
+      # Ensure ffmpeg-full mount point exists.
+      - "mkdir -p \"${FLATPAK_DEST}/lib/ffmpeg\""