feat(gate): foreground caption fetches take priority over the background sweep (ADR-026)

A user waiting on a Summarize click shared the per-IP caption gate equally with
the background firehose, so on a busy IP the click was slow or 429'd. Add a
context-marked priority lane: the web path (engineProcessor.ProcessVideo) marks
its context foreground; the gate serves foreground immediately while background
fetches yield until no foreground is pending. Threaded via a context value (no
new signatures) + a process-wide foregroundPending counter. Clicks are rare, so
the background barely loses throughput; the waiting human gets the cleaner slot.

Drops the credentials probe: ADR-010 and captions.go already settle it — the
timedtext/InnerTube path rejects authenticated requests and the OAuth token does
not authenticate it anyway, so auth cannot help and can hurt. Documented in
ADR-026 rather than built.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

internal/adapters/youtube/gate_test.go

@@ -82,3 +82,37 @@ func TestSetFetchRateZeroIsUnlimited(t *testing.T) {
 		require.NoError(t, WaitFetchGate(context.Background()))
 	}
 }
+
+func TestForegroundContextMarker(t *testing.T) {
+	require.False(t, isForeground(context.Background()), "plain context is background")
+	require.True(t, isForeground(ForegroundContext(context.Background())), "marked context is foreground")
+}
+
+// TestWaitFetchGateForegroundProceedsImmediately: a foreground fetch acquires a
+// token without yielding, even when background callers exist.
+func TestWaitFetchGateForegroundProceedsImmediately(t *testing.T) {
+	SetFetchRate(0) // unlimited limiter — isolate the yield logic from pacing
+	foregroundPending.Store(0)
+	t.Cleanup(func() { foregroundPending.Store(0) })
+
+	ctx, cancel := context.WithTimeout(context.Background(), time.Second)
+	defer cancel()
+	require.NoError(t, WaitFetchGate(ForegroundContext(ctx)), "foreground proceeds immediately")
+}
+
+// TestWaitFetchGateBackgroundYieldsToForeground: while a foreground fetch is
+// pending, a background fetch yields (does not take a token) until the foreground
+// clears — proven by a background wait timing out against its own deadline, then
+// succeeding once the foreground is done.
+func TestWaitFetchGateBackgroundYieldsToForeground(t *testing.T) {
+	SetFetchRate(0)
+	foregroundPending.Store(1) // simulate a foreground fetch in flight
+	t.Cleanup(func() { foregroundPending.Store(0) })
+
+	ctx, cancel := context.WithTimeout(context.Background(), 250*time.Millisecond)
+	defer cancel()
+	require.Error(t, WaitFetchGate(ctx), "background yields (blocks) while foreground is pending")
+
+	foregroundPending.Store(0) // foreground done
+	require.NoError(t, WaitFetchGate(context.Background()), "background proceeds once foreground clears")
+}