Give PATH and yt-dlp the verified FFmpeg, and split the e2e job

[thcp]

Closes #651
Closes #684
Closes #686

What was wrong

The backend had two separate answers to "which FFmpeg".

• Separation used the pair setup verified. The desktop shell passes it in STEMDECK_FFMPEG and STEMDECK_FFPROBE.
• PATH and yt-dlp were given FFMPEG_DIR. In a desktop install that is always data/ffmpeg, whatever setup concluded about it.

That broke YouTube imports in two situations.

• An FFmpeg that setup rejected is still what yt-dlp gets, and still first on PATH #651: setup rejected the data-directory copy (an Intel pair on Apple Silicon, or a build missing an encoder) and settled on another. PATH and yt-dlp kept using the rejected copy, and the error named a binary the app had supposedly stopped using.
• YouTube imports have no FFmpeg when it is installed under data/ffmpeg/bin #684: the FFmpeg lives under data/ffmpeg/bin/, a layout setup accepts. yt-dlp was handed data/ffmpeg, which holds no binary. yt-dlp runs dir/ffmpeg literally and never falls back to PATH, so it had no FFmpeg at all.

The fix

ffmpeg_dir() in app/core/config.py gives the directory of the ffmpeg this process actually runs, provided ffprobe sits beside it. Both configure_portable_environment() (PATH) and _base_ydl_opts() (yt-dlp) now use it.

yt-dlp takes one directory and looks for both binaries there. So when ffmpeg and ffprobe are in different places, no directory is handed over and PATH decides. The shell has already put the verified FFmpeg first on PATH.

Setup	yt-dlp location, before	After
Data-directory FFmpeg verified	data/ffmpeg	data/ffmpeg
Data-directory copy rejected (#651)	the rejected copy	the verified FFmpeg's directory
Nested bin/ layout (#684)	data/ffmpeg, no binary	data/ffmpeg/bin
Docker, source with FFmpeg on PATH	none	none
STEMDECK_FFMPEG_DIR set by hand	that directory	that directory

The FFmpeg directory in use is logged at startup. So is a data-directory FFmpeg that is being skipped, since the failure this prevents was silent. Nothing is deleted: the rejected copy stays where it is, as #643 intends. No Rust change and no new environment variable.

Also: split the e2e job across three runners (#686)

The frontend-e2e job took about six minutes, running one test at a time. It has to stay serial within a run, because the suite shares one backend and one jobs directory and several specs change server state, so raising workers would cause intermittent failures. It now runs as three shards. Each shard is its own runner with its own backend, so nothing is shared. Files stay whole within a shard, one failing shard does not cancel the others, and each uploads its report under its own name. No required status check names frontend-e2e, so the per-shard names block nothing.

Run locally, each shard against a fresh server: 87, 90 and 81 tests, the full 258, all passing. No spec depends on another file's leftovers.

Verification

• Cold start with the An FFmpeg that setup rejected is still what yt-dlp gets, and still first on PATH #651 environment (a rejected pair in the data directory, the verified one elsewhere): main gives yt-dlp data\ffmpeg, the rejected copy; this branch gives it the verified directory.
• 9 new tests over real files, all failing against main. They cover the rejected-copy case for the directory, PATH, yt-dlp and the log line; the nested layout; and the four setups that have to keep working.
• Full pytest suite: 1,089 pass. The one failure needs the optional allin1_infer package, which is missing locally and present in CI.
• ruff, bandit and uv.lock are clean.