Implement sync_logic.py and ffmpeg_export.py (build order steps 2-3)

sync_logic.py: pure delay_ms computation with the documented sign
convention. Caught and fixed a sign error in my own test-fixture
ground-truth doc while writing the unit tests: the audio+350ms fixture
actually requires delay_ms=-350 (delay video), not +350, since the
audio is already the late one.

ffmpeg_export.py: ports ffdelay's two-branch command structure
(offset video input vs audio input depending on delay_ms sign) plus
its documented quirks (leading-zero float formatting, -ss/-t applied
to both inputs for clip mode, non-fatal stream-copy warnings surfaced
via stderr rather than swallowed).

Added an end-to-end integration test (scripts/test_export_roundtrip.py)
that independently re-detects event timing in the exported output via
ffmpeg scene-change/silence detection (not the same code path used to
build the export) and confirms both the positive- and negative-delay
branches bring drift down from ~350ms to under 1ms.

test_media/README.md

@@ -10,14 +10,24 @@ validating marker capture, offset math, and lossless export.
 - `sync_test_OUTOFSYNC_audio+350ms.mp4` — same content, but the audio track has
   been shifted +350ms later relative to video (via `-itsoffset 0.350` on the audio
   input, stream-copied). The flash event stays at video t=5.000s; the beep event
-  now appears at t=5.350s.
+  now appears at t=5.350s. Exercises the negative-delay_ms / "delay video" branch
+  in ffmpeg_export.py.
+
+- `sync_test_OUTOFSYNC_video+350ms.mp4` — same content, but the *video* track has
+  been shifted +350ms later instead (via `-itsoffset 0.350` on the video input).
+  The beep stays at audio t=5.000s; the flash now appears at t=5.350s. Exercises
+  the positive-delay_ms / "delay audio" branch in ffmpeg_export.py.
 
 **Ground truth for the app's marker/offset workflow:**
 - Mark Video at the flash → ~5.000s
 - Mark Audio at the beep → ~5.350s
-- Expected computed `delay_ms` = +350 (audio needs to be delayed to match video)
-- Exporting `sync_test_OUTOFSYNC_audio+350ms.mp4` with delay_ms = +350 should
-  reproduce (bit-for-bit, modulo container overhead) `sync_test_INSYNC.mp4`'s sync.
+- Expected computed `delay_ms` = (video_mark - audio_mark) * 1000 = **-350**
+  (audio is already the *late* one here, so the fix is to delay the video by
+  350ms to catch up to it -- not to delay the audio further. Negative
+  delay_ms → offset the video input, per sync_logic.py's sign convention.)
+- Exporting `sync_test_OUTOFSYNC_audio+350ms.mp4` with delay_ms = -350 should
+  land both events at t=5.350s in the output (not back at 5.000s -- the
+  absolute timeline shifts, only the *relative* sync matters).
 
 Frame at exactly t=5.000s is frame index 150 (30fps) — useful for checking
 frame-step precision lands exactly on it.