fix(ui): the page's end scrolls out from under Back to top

The button floats over the bottom-right corner, and at the end of a long table it covered the closing
pager's '100' and 'All'. While it is up, PageScroller ends the page a button's height later (only
then, so a full-height layout gets no scrollbar). Its shown state is a shared store read through a
use… wrapper: a store's .use() called straight from a component is memoized by the React Compiler
and never re-renders (contract: store.contract.test.ts).

frontend/src/lib/store.contract.test.ts

@@ -0,0 +1,25 @@
+import { readdirSync, readFileSync } from "node:fs";
+import { describe, expect, it } from "vitest";
+
+// A store's `.use()` is a hook the React Compiler cannot see: its name is a method's, not `use…`'s.
+// Called straight from a COMPONENT, the compiled render memoized its result and never re-rendered on
+// a change — Back to top stayed hidden (E28 UAT, measured under vitest's compiler build). Inside a
+// function named `use…` it is compiled as a hook and works, so that is the only place it may be read.
+describe("a store's use()", () => {
+  it("is read only inside a function named use…", () => {
+    const root = new URL("../", import.meta.url);
+    const offenders: string[] = [];
+    for (const f of readdirSync(root, { recursive: true, encoding: "utf8" })) {
+      if (!/\.tsx?$/.test(f) || f.includes(".test.")) continue;
+      const src = readFileSync(new URL(f.replace(/\\/g, "/"), root), "utf8");
+      for (const m of src.matchAll(/\b\w+\.use\(\)/g)) {
+        const before = src.slice(0, m.index);
+        const owners = [...before.matchAll(/(?:function\s+(\w+)|const\s+(\w+)\s*=\s*\()/g)];
+        const owner = owners.at(-1);
+        const name = owner?.[1] ?? owner?.[2] ?? "";
+        if (!name.startsWith("use")) offenders.push(`${f}: ${m[0]} in ${name || "?"}`);
+      }
+    }
+    expect(offenders).toEqual([]);
+  });
+});