feat(web): mode-aware backlog banner — stop telling manual users summaries auto-arrive

The first pilot user sat in Manual mode reading "new summaries land gradually,
check back tomorrow" — copy that only makes sense in Automatic mode. Manual mode
never auto-summarizes, so the banner promised delivery that would never come.

The list page now reads the user's summarize mode and shows mode-correct copy:
- Auto: unchanged "land gradually" backlog note.
- Manual: "new videos appear here but are not summarized automatically — use the
  Summarize button" plus a "Switch to Automatic" link to /account.
The connected-but-empty first-run state is likewise mode-aware.

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

internal/web/handlers.go

@@ -233,11 +233,20 @@ func (a *App) handleList(w http.ResponseWriter, r *http.Request) {
 	}
 	hasConnected := len(conns) > 0
 
-	if isHTMX(r) {
-		a.render(w, r, summaryList(buckets, hasConnected))
+	// Summarization mode drives the backlog copy: an auto user is told summaries
+	// land gradually; a manual user is told to click Summarize (the first pilot
+	// user sat in manual mode reading "land automatically" and waited forever).
+	autoSummarize, err := a.Store.GetAutoSummarize(r.Context(), userID)
+	if err != nil {
+		a.serverError(w, r, "summarize mode", err)
 		return
 	}
-	a.render(w, r, ListPage(buckets, f, stats, takeFlash(w, r), hasConnected, channels))
+
+	if isHTMX(r) {
+		a.render(w, r, summaryList(buckets, hasConnected, autoSummarize))
+		return
+	}
+	a.render(w, r, ListPage(buckets, f, stats, takeFlash(w, r), hasConnected, channels, autoSummarize))
 }
 
 // handleDetail renders one summary in full (highlights, takeaways, action group).