Avoid repeating entries until all have been picked

[reinsch82]

Summary

• Replace pure random selection with a shuffle bag: every entry is picked exactly once per round before any entry can repeat
• Persist the remaining pool in localStorage (keyed by the sorted item set), so reloads continue the current round instead of repeating — relevant since the page auto-picks on load
• Prevent a new round from starting with the same entry the previous round ended on, so the same name never appears twice in a row
• Show a 🔄 marker on the last pick of each round
• Add a Reset button that clears the stored pool for the current item set only

Testing

• Verified the pick logic with a 10,000-pick simulation: each round covers all items exactly once, with no back-to-back repeats
• Manual check: python3 -m http.server and open http://localhost:8000/?items=Alice,Bob,Carol,Dave