feat(ux): auto-advance on game type and race selection

- Step 4: selecting a game type immediately advances to step 5
- Step 5: selecting Endlos or a quick-pick number immediately finalizes race-to

Improves flow by removing an extra click. No changes to validation.

Refs #26

src/components/NewGame.tsx

@@ -612,6 +612,8 @@ const GameTypeStep = ({ onNext, onCancel, initialValue = '' }: GameTypeStepProps
 
   const handleSelect = (selectedType: string) => {
     setGameType(selectedType);
+    // Auto-advance to next step on selection
+    onNext(selectedType);
   };
 
   const handleSubmit = (e: Event) => {
@@ -706,7 +708,11 @@ const RaceToStep = ({ onNext, onCancel, initialValue = '', gameType }: RaceToSte
 
   const handleQuickPick = (value: number) => {
     // For endlos (endless) games, use Infinity to prevent automatic completion
-    setRaceTo(value === 0 ? 'Infinity' : value);
+    const selected = value === 0 ? 'Infinity' : value;
+    setRaceTo(selected);
+    // Auto-advance to the next step (finalize) when a quick pick is chosen
+    const raceToValue = selected === 'Infinity' ? Infinity : (parseInt(String(selected), 10) || 0);
+    onNext(raceToValue);
   };
 
   const handleInputChange = (e: Event) => {