Update auto-broadcast completion logic for tournaments

Refine tournament auto-broadcast detection algorithm to handle
multi-page tournaments more robustly. Specifically:

- Improve completion detection for multi-page tournaments - Prevent
false completion when cycling through pages - Add more descriptive
logging for edge cases

tournaments/templates/tournaments/broadcast/broadcasted_auto.html

@@ -266,8 +266,9 @@
             const pageCount = data.pageCount();
             const elapsed = Date.now() - startTime;
 
+            // Skip tournaments with no pages (this shouldn't happen now, but just in case)
             if (pageCount === 0) {
-                console.log('No pages to display yet');
+                console.log('Tournament has no content, should have been filtered out');
                 return;
             }
 
@@ -289,10 +290,12 @@
                     reason = 'Single page - 15 seconds elapsed';
                 }
             } else if (pageCount > 1) {
-                // Multi-page tournament: complete when we cycle back to page 1 after seeing all pages
-                if (currentActive === 1 && lastActive > 1 && maxPagesSeen >= pageCount) {
+                // Multi-page tournament: complete when we're about to go back to page 1 after seeing all pages
+                // Check if we're at the last page and have seen all pages
+                if (currentActive === pageCount && maxPagesSeen >= pageCount && lastActive !== null) {
+                    // We're at the last page and have seen all pages - complete now before going back to page 1
                     shouldComplete = true;
-                    reason = 'Multi-page - full cycle completed';
+                    reason = 'Multi-page - completed at last page (avoiding first page repeat)';
                 } else if (elapsed >= completionTime) {
                     // Fallback: complete after (pageCount * 15 seconds)
                     shouldComplete = true;