fix(docker): install system ffmpeg on Alpine, drop broken bundled binary

Video uploads on production fail with "missing ffmpeg" because the
backend container ships nothing usable for the video pipeline.

Two compounding causes:

1. **Alpine + glibc mismatch.** The npm `@ffmpeg-installer/ffmpeg`
   dependency added with the video-support PR (commit 68a9dc5)
   ships per-platform binaries via optionalDependencies. The Linux
   binaries are built against glibc, but the backend image runs on
   `node:22-alpine` (musl libc) — known to either fail to execute
   or fail on shared-library lookups on Alpine.

2. **`ffprobe` missing entirely.** `@ffmpeg-installer/ffmpeg`
   bundles only the `ffmpeg` binary. There's a separate
   `@ffprobe-installer/ffprobe` package that the codebase never
   depended on. But `videoProcessor.js:21` calls
   `ffmpeg.ffprobe(videoPath, …)` — the very first step of the
   video pipeline shells out to a `ffprobe` binary that doesn't
   exist in the image. Even if (1) worked, every video upload
   would 500 here.

The fix is to install Alpine's `ffmpeg` package via apk. It ships
both `ffmpeg` and `ffprobe` built natively against musl, ~70MB
extra image size, single line in the Dockerfile, no per-arch
handling needed (apk pulls the right binary for both linux/amd64
and linux/arm64 — works with the multi-arch infra from #349).

- `backend/Dockerfile`: add `ffmpeg` to the apk install line.
- `backend/Dockerfile.dev`: same for dev parity.
- `backend/src/services/videoProcessor.js`: remove the
  `setFfmpegPath(require('@ffmpeg-installer/ffmpeg').path)` line
  — without removing it, fluent-ffmpeg would prefer the broken
  bundled binary over the working apk one. Letting fluent-ffmpeg
  fall back to PATH lookup picks up the apk binary in the
  container and the developer's locally-installed binary on dev
  hosts (Homebrew on macOS, apt on Debian).
- `backend/package.json`: drop the now-unused
  `@ffmpeg-installer/ffmpeg` dependency. `npm install` removes
  2 packages from the lockfile.

Verified: `videoProcessor.js` still loads cleanly (`node -e
"require('./src/services/videoProcessor')"`); lint clean.

backend/Dockerfile.dev

@@ -5,8 +5,10 @@ WORKDIR /app
 # Upgrade all packages to fix security vulnerabilities (BusyBox CVEs)
 RUN apk upgrade --no-cache
 
-# Install dumb-init for proper signal handling
-RUN apk add --no-cache dumb-init
+# Install dumb-init for proper signal handling and ffmpeg for video uploads.
+# Alpine's ffmpeg ships both ffmpeg + ffprobe built natively against musl;
+# the npm-bundled binary doesn't run reliably on Alpine. Match production.
+RUN apk add --no-cache dumb-init ffmpeg
 
 # Copy package files
 COPY package*.json ./