feat(server): add public list pagination constants and page normalizer

Made-with: Cursor

server/constants/public-profile-lists.ts

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+/** 公开主页 profile 聚合接口中每类预览条数 */
+export const PUBLIC_PREVIEW_LIMIT = 5;
+
+/** 公开列表子页每页条数（仅服务端使用） */
+export const PUBLIC_LIST_PAGE_SIZE = 10;

server/utils/public-pagination.test.ts

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+import { describe, expect, test } from "bun:test";
+import { normalizePublicListPage } from "./public-pagination";
+
+describe("normalizePublicListPage", () => {
+  test("returns 1 for non-finite or invalid input", () => {
+    expect(normalizePublicListPage(undefined)).toBe(1);
+    expect(normalizePublicListPage(null)).toBe(1);
+    expect(normalizePublicListPage("")).toBe(1);
+    expect(normalizePublicListPage("abc")).toBe(1);
+    expect(normalizePublicListPage(NaN)).toBe(1);
+    expect(normalizePublicListPage(Infinity)).toBe(1);
+    expect(normalizePublicListPage(-Infinity)).toBe(1);
+    expect(normalizePublicListPage({})).toBe(1);
+  });
+
+  test("returns 1 for values less than 1", () => {
+    expect(normalizePublicListPage(0)).toBe(1);
+    expect(normalizePublicListPage(-1)).toBe(1);
+    expect(normalizePublicListPage(-3.5)).toBe(1);
+    expect(normalizePublicListPage("0")).toBe(1);
+    expect(normalizePublicListPage("-1")).toBe(1);
+  });
+
+  test("returns positive integers unchanged (or parsed)", () => {
+    expect(normalizePublicListPage(1)).toBe(1);
+    expect(normalizePublicListPage(42)).toBe(42);
+    expect(normalizePublicListPage("5")).toBe(5);
+    expect(normalizePublicListPage("10")).toBe(10);
+  });
+
+  test("floors positive floats", () => {
+    expect(normalizePublicListPage(2.7)).toBe(2);
+    expect(normalizePublicListPage(3.99)).toBe(3);
+    expect(normalizePublicListPage(1.0001)).toBe(1);
+  });
+});

server/utils/public-pagination.ts

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+/**
+ * 解析公开列表的 ?page= query：非有限数或 <1 时返回 1；否则返回正整数（float 向下取整）。
+ */
+export function normalizePublicListPage(raw: unknown): number {
+  const n =
+    typeof raw === "string"
+      ? Number.parseInt(raw, 10)
+      : typeof raw === "number"
+        ? raw
+        : Number.NaN;
+  if (!Number.isFinite(n) || n < 1) {
+    return 1;
+  }
+  return Math.floor(n);
+}