feat(youtube): process-wide caption-fetch rate gate (ADR-014 item 2)

ADR-014 item 2 — a single per-egress-IP rate gate shared by every caption
fetch — was specced but only per-video backoff (rate_limited_at) shipped.
Build the real gate now: it is load-bearing once ADR-018 puts auto-summarize
on an in-process schedule across multiple users (all fetches leave one pod's
egress IP, concurrently with live "Summarize" clicks — without a shared gate
that self-inflicts 429s every cycle).

globalFetchGate (golang.org/x/time/rate, default 2s/req burst 1) is consulted
in httpDo before every live outbound fetch — player, watch-page, timedtext —
so the scheduler runners and the web click-path serialise through one limiter
regardless of how many users/goroutines are upstream. The test seam
(a.transport != nil) skips the gate so fakes are not throttled.

TAPIR_FETCH_RATE (Go duration, default 2s, 0 = unlimited) wires SetFetchRate in
cmdRun; the existing per-video backoff stays as the complementary 429 handler.

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

internal/config/config.go

@@ -65,6 +65,17 @@ type Config struct {
 	// expires the video is retried. Zero means "always retry" (no backoff).
 	FetchBackoff time.Duration
 
+	// FetchRate is the minimum interval between outbound caption fetches across the
+	// whole process — the shared per-egress-IP rate gate (ADR-014 item 2). It is
+	// the gate that makes auto-summarize-on-a-schedule safe: scheduler runners and
+	// the web click-path serialise through it. Zero = unlimited (dev/tests).
+	FetchRate time.Duration
+
+	// DiscoveryInterval, when > 0, makes `serve` run in-process scheduled discovery
+	// for ALL users on that cadence (ADR-018). Zero/unset = disabled, so dev and
+	// tests never auto-fetch. Single-replica assumption — see cmdServe.
+	DiscoveryInterval time.Duration
+
 	// HTTPAddr is the listen address for `tapir serve` (the Stage-0 web UI).
 	HTTPAddr string
 
@@ -97,6 +108,7 @@ const (
 	defaultOAuthRedirectAddr    = "localhost:8080"
 	defaultHTTPAddr             = ":8080"
 	defaultFetchBackoff         = time.Hour
+	defaultFetchRate            = 2 * time.Second
 	defaultPublicURL            = "https://tapir.d-ma.be"
 )
 
@@ -144,6 +156,18 @@ func Load() (Config, error) {
 	}
 	c.FetchBackoff = backoff
 
+	fetchRate, err := durationOr("TAPIR_FETCH_RATE", defaultFetchRate)
+	if err != nil {
+		return Config{}, err
+	}
+	c.FetchRate = fetchRate
+
+	discovery, err := durationOr("TAPIR_DISCOVERY_INTERVAL", 0)
+	if err != nil {
+		return Config{}, err
+	}
+	c.DiscoveryInterval = discovery
+
 	return c, nil
 }