feat(usecase): implement ProcessNewVideo core path

Resolve transcript -> summarize -> deliver, or skip when no usable
transcript. Sinks fail independently: a failing sink does not abort the
others and successful deliveries are kept; per-sink errors are returned
joined. Makes the two scaffolded acceptance scenarios GREEN.

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

internal/usecase/engine.go

@@ -11,6 +11,7 @@ package usecase
 import (
 	"context"
 	"errors"
+	"fmt"
 
 	"gitea.d-ma.be/mathias/tapir/internal/domain"
 	"gitea.d-ma.be/mathias/tapir/internal/ports"
@@ -43,5 +44,29 @@ type ProcessResult struct {
 // resolve transcript -> (summarize -> deliver) | skip.
 // See docs/use-cases/summarize_new_video.feature.
 func (e *Engine) ProcessNewVideo(ctx context.Context, v domain.Video) (ProcessResult, error) {
-	return ProcessResult{}, ErrNotImplemented
+	t, err := e.Source.FetchTranscript(ctx, v)
+	if err != nil {
+		return ProcessResult{Video: v}, fmt.Errorf("fetch transcript: %w", err)
+	}
+	if !t.HasText() {
+		// No usable transcript: record the skip, produce no summary, deliver nothing
+		// (captions-first, ADR-007; the watcher uses this to avoid reprocessing).
+		return ProcessResult{Video: v, Skipped: true, Reason: "no transcript"}, nil
+	}
+
+	sum, err := e.AI.Summarize(ctx, v, t)
+	if err != nil {
+		return ProcessResult{Video: v}, fmt.Errorf("summarize: %w", err)
+	}
+
+	// Sinks fail independently: a failing sink must not abort the others, and
+	// successful deliveries are not dropped. Collect every error, return them joined.
+	var errs []error
+	for _, sink := range e.Sinks {
+		if err := sink.Deliver(ctx, sum); err != nil {
+			errs = append(errs, fmt.Errorf("deliver to %s: %w", sink.Name(), err))
+		}
+	}
+
+	return ProcessResult{Video: v, Summary: &sum}, errors.Join(errs...)
 }