fix(抽奖): 概率按 weight/1000 显示与录入（支持小数%，总权重100000=100%）

- prize-grid: 概率预览/合计/卡片改用 weightToPercent(weight/1000)，
  合计校验对齐 FULL_TOTAL_WEIGHT=100000；修正原来把原始 weight 当 % 显示（如 49901%）
- prize-form: 概率输入按百分比(0-100，step 0.001)，提交 ×1000 存 weight，回填 ÷1000

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

apps/admin/src/sections/lottery/prize-grid.tsx

@@ -14,9 +14,16 @@ import PrizeForm from "./prize-form";
 
 const DEFAULT_GRID_SIZE = 9;
 const CENTER_SLOT = 4;
-const PERCENT_DECIMALS = 1;
-const REQUIRED_TOTAL_PERCENT = 100;
 const CENTS_PER_YUAN = 100;
+// 概率单位约定：weight 1000 = 1%，总权重 100000 = 100.000%（支持 3 位小数概率）。
+const WEIGHT_PER_PERCENT = 1000;
+const FULL_TOTAL_WEIGHT = 100 * WEIGHT_PER_PERCENT;
+
+// weightToPercent 把原始 weight 转成百分比字符串（最多 3 位小数，去尾零）。
+function weightToPercent(weight: number): string {
+  const pct = weight / WEIGHT_PER_PERCENT;
+  return `${Number.parseFloat(pct.toFixed(3))}`;
+}
 
 interface PrizeGridProps {
   activity: API.LotteryActivity;
@@ -110,7 +117,7 @@ export default function PrizeGrid({ activity }: PrizeGridProps) {
     [randomPrizes]
   );
   const hasFallback = prizes.some((prize) => prize.is_fallback);
-  const totalIsValid = totalWeight === REQUIRED_TOTAL_PERCENT;
+  const totalIsValid = totalWeight === FULL_TOTAL_WEIGHT;
   const gridSize = activity.grid_size || DEFAULT_GRID_SIZE;
   const slots = Array.from({ length: gridSize }, (_, index) => index);
 
@@ -137,7 +144,8 @@ export default function PrizeGrid({ activity }: PrizeGridProps) {
           </p>
           {randomPrizes.length > 0 && (
             <Badge variant={totalIsValid ? "secondary" : "destructive"}>
-              {t("prize.probabilityTotal", "Total")}: {totalWeight}%
+              {t("prize.probabilityTotal", "Total")}:{" "}
+              {weightToPercent(totalWeight)}%
             </Badge>
           )}
         </div>
@@ -145,9 +153,7 @@ export default function PrizeGrid({ activity }: PrizeGridProps) {
           <div className="flex flex-wrap gap-2">
             {randomPrizes.map((prize) => (
               <Badge key={prize.id} variant="secondary">
-                {prize.name}:{" "}
-                {((prize.weight / totalWeight) * 100).toFixed(PERCENT_DECIMALS)}
-                %
+                {prize.name}: {weightToPercent(prize.weight)}%
               </Badge>
             ))}
           </div>
@@ -170,7 +176,7 @@ export default function PrizeGrid({ activity }: PrizeGridProps) {
             {t(
               "prize.totalNot100Hint",
               "The drawable prizes currently total {{total}}%. Adjust each prize's win probability so they sum to exactly 100%.",
-              { total: totalWeight }
+              { total: weightToPercent(totalWeight) }
             )}
           </AlertDescription>
         </Alert>
@@ -244,8 +250,10 @@ export default function PrizeGrid({ activity }: PrizeGridProps) {
                   })()}
                   <span className="text-muted-foreground text-xs">
                     {t("prize.weightShort", "Prob")}:{" "}
-                    {prize.is_fallback ? "—" : `${prize.weight}%`} ·{" "}
-                    {t("prize.stockShort", "Stock")}:{" "}
+                    {prize.is_fallback
+                      ? "—"
+                      : `${weightToPercent(prize.weight)}%`}{" "}
+                    · {t("prize.stockShort", "Stock")}:{" "}
                     {prize.total_stock === null ? "∞" : prize.total_stock}
                   </span>
                   <div className="flex flex-wrap justify-center gap-1">