fix(stream): functional libplacebo probe + benchmark hardening

Review (critico) caught a regression: the prod agent image ships a BtbN GPL
ffmpeg with libplacebo COMPILED IN but no Vulkan runtime (debian-slim, no
libvulkan1/mesa-vulkan-drivers/nvidia ICD). The presence probe (ffmpeg
-filters) would flip HasLibplacebo on, the filter's Vulkan device creation
would fail at runtime, and HDR sources that previously tonemapped via zscale
would break.

- FFmpegSupportsLibplacebo now RUNS the filter on one synthetic frame and
  requires a clean exit (forces Vulkan device init + filtergraph negotiation),
  so it is honest about THIS host: works on Vulkan-capable hosts, falls back to
  zscale where Vulkan is absent. Logs the real ffmpeg error on failure.
- Warm the libplacebo (Vulkan init ~1.7s) + zscale caches in a background
  goroutine at startup so the first stream session doesn't pay the probe and
  risk its setup timeout.
- Benchmark: margin 1.5x -> 2.0x (the probe measures encode only; real decode
  of HEVC/10-bit + busier content needs more headroom), per-probe timeout
  12s -> 6s + overall 45s -> 20s (it blocks registration on software hosts),
  and a 'no rung measured' case (missing lavfi/wedged ffmpeg) now keeps the
  1080 default instead of flooring at 480 — an infra failure isn't a slow host.

Verified e2e on the fixed binary: LOTR Two Towers (HEVC 3840x1608 10-bit
HDR10/PQ, 12GB) on desktop-Chrome caps -> hls, ffmpeg runs h264_nvenc with
-vf ...,libplacebo=...:format=yuv420p:tonemapping=bt.2390 (zscale chain
replaced), 45 fMP4 segments, ffprobe confirms output h264 yuv420p bt709
(tonemapped from bt2020/smpte2084), no ffmpeg errors.

internal/engine/tonemap_test.go

@@ -2,6 +2,7 @@ package engine
 
 import (
 	"os"
+	"os/exec"
 	"path/filepath"
 	"strings"
 	"testing"
@@ -112,6 +113,22 @@ func TestTonemap_VAAPIInsertsBeforeHwupload(t *testing.T) {
 	}
 }
 
+func TestFFmpegSupportsLibplacebo_FunctionalProbe(t *testing.T) {
+	if FFmpegSupportsLibplacebo("") {
+		t.Error("empty path must be false")
+	}
+	// A bogus path can't run → false (no panic, no hang).
+	if FFmpegSupportsLibplacebo("/nonexistent/ffmpeg") {
+		t.Error("nonexistent ffmpeg must be false")
+	}
+	// With a real ffmpeg the result is environment-dependent (true only when a
+	// Vulkan runtime is present), so we only assert the probe completes and
+	// returns a bool — its whole purpose is to be honest about THIS host.
+	if _, err := exec.LookPath("ffmpeg"); err == nil {
+		_ = FFmpegSupportsLibplacebo("ffmpeg") // must not hang or panic
+	}
+}
+
 func TestFFmpegSupportsZscale_Stub(t *testing.T) {
 	dir := t.TempDir()