feat(web): Processor port + in-flight ProcessingSet on App

Add the seam for immediate web-triggered summarization. Processor is the
optional single-video summarize port (nil = queue-only, unchanged behaviour);
ProcessingSet is an ephemeral, concurrency-safe set of in-flight (user,video)
ids so a status endpoint can show progress until the summary lands. State is
deliberately in-memory only — the DB holds the durable truth across restarts.

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

internal/web/processing.go

@@ -0,0 +1,42 @@
+package web
+
+import (
+	"context"
+	"sync"
+)
+
+// Processor runs the core summarization use case for a single already-discovered
+// video — resolve its transcript, summarize, deliver to the store. *usecase.Engine
+// wrapped with the store satisfies it (wired in cmd/tapir). Optional on App: a nil
+// Processor means queue-only — the "Summarize" button only flips the DB flag and
+// the next `tapir run` does the work.
+type Processor interface {
+	ProcessVideo(ctx context.Context, userID, videoID string) error
+}
+
+// ProcessingSet tracks the (user, video) ids currently being summarized in-process
+// so the status endpoint can show the animation until the summary lands. It is
+// ephemeral (single-instance Stage-1): a restart drops it, and the DB holds the
+// durable state — the summary is present, or summarize_requested is still set so
+// `tapir run` retries. The zero value is ready to use; methods are concurrency-safe.
+type ProcessingSet struct {
+	m sync.Map
+}
+
+// Add marks a key in-flight.
+func (p *ProcessingSet) Add(key string) { p.m.Store(key, struct{}{}) }
+
+// Remove clears a key once its summarization finishes (success or failure).
+func (p *ProcessingSet) Remove(key string) { p.m.Delete(key) }
+
+// Has reports whether a key is currently in-flight.
+func (p *ProcessingSet) Has(key string) bool {
+	_, ok := p.m.Load(key)
+	return ok
+}
+
+// processingKey scopes the in-flight key by user so one user's summarization is
+// never confused with another's for the same video id.
+func processingKey(userID, videoID string) string {
+	return userID + "|" + videoID
+}