fix(public): unify family representative selection with detail endpoint

List/home endpoints picked the family representative row via goods[0],
which drifted with the list sort parameter (cheapest under PRICE_ASC,
lowest id under DEFAULT ties), causing goodName and other
representative-derived fields to differ from the detail endpoint.
Extract pickFamilyRepresentative (goodPriority desc -> createdAt desc
-> id asc, same as getGoodByFamilyId) and use it in getGoods and
getHomeGoods grouping. Group ordering and API contracts unchanged.

apps/api/src/public/public.service.ts

@@ -254,7 +254,7 @@ export class PublicService {
       else grouped.set(key, [good]);
     }
     let items = [...grouped.values()].map((goods) => {
-      const rep = goods[0];
+      const rep = this.pickFamilyRepresentative(goods);
       const dto = this.toPublicGood(rep);
       // 列表价 = 族矩阵最低价（"这个款之下有哪些价格"的起价）；无矩阵回退链接价
       const familyMin = rep.familyId
@@ -421,16 +421,20 @@ export class PublicService {
       take: query.limit,
     });
     const familyMinPrices = await this.loadFamilyMinPrices();
-    // 首页同样按族去重（同族多条位置配置只保留排序最前一条），再截取 limit
-    const seen = new Set<string>();
-    const items: PublicGoodDto[] = [];
+    // 首页同样按族去重（一族只出一条），代表行选取与详情/列表一致
+    const grouped = new Map<string, PublicGoodListRow[]>();
     for (const good of rows) {
       const key = good.familyId ? `f:${good.familyId}` : `g:${good.id}`;
-      if (seen.has(key)) continue;
-      seen.add(key);
-      const dto = this.toPublicGood(good);
-      const familyMin = good.familyId
-        ? familyMinPrices.get(good.familyId.toString())
+      const bucket = grouped.get(key);
+      if (bucket) bucket.push(good);
+      else grouped.set(key, [good]);
+    }
+    const items: PublicGoodDto[] = [];
+    for (const goods of grouped.values()) {
+      const rep = this.pickFamilyRepresentative(goods);
+      const dto = this.toPublicGood(rep);
+      const familyMin = rep.familyId
+        ? familyMinPrices.get(rep.familyId.toString())
         : undefined;
       if (familyMin !== undefined) dto.price = familyMin;
       items.push(dto);
@@ -438,6 +442,22 @@ export class PublicService {
     return items.slice(0, query.limit);
   }
 
+  /**
+   * 族代表行选取：与详情 getGoodByFamilyId 的 orderBy 保持一致
+   * （goodPriority desc → createdAt desc → id asc），
+   * 保证列表/首页与详情返回的 goodName、主图、分类等代表行字段一致。
+   */
+  private pickFamilyRepresentative<T extends { goodPriority: number | null; createdAt: Date; id: bigint }>(
+    goods: T[],
+  ): T {
+    return [...goods].sort(
+      (a, b) =>
+        (b.goodPriority ?? 0) - (a.goodPriority ?? 0) ||
+        b.createdAt.getTime() - a.createdAt.getTime() ||
+        (a.id < b.id ? -1 : a.id > b.id ? 1 : 0),
+    )[0];
+  }
+
   /** 入参用精简行类型：列表（PublicGoodListRow）与详情（PublicGoodRow，字段超集）都能传 */
   private toPublicGood(good: PublicGoodListRow): PublicGoodDto {
     const formatGroup = (group: { id: bigint; groupName: string; sortOrder: number } | null) =>