feat: apply our exisitng icons to engage sidebar

src/seqta/utils/waitForEngageMenuList.ts

@@ -0,0 +1,39 @@
+import { waitForElm } from "@/seqta/utils/waitForElm";
+
+/** Engage mounts the sidebar inside batched React trees; polling `waitForElm` matches the real DOM reliably. */
+export async function waitForEngageMenuList(): Promise<HTMLElement | null> {
+  const poll = true as const;
+  const interval = 100;
+  const trySelectors: { selector: string; maxIterations: number }[] = [
+    { selector: "#menu > ul > li", maxIterations: 500 },
+    { selector: "#menu ul", maxIterations: 350 },
+    { selector: "#menu", maxIterations: 350 },
+  ];
+
+  for (const { selector, maxIterations } of trySelectors) {
+    try {
+      await waitForElm(selector, poll, interval, maxIterations);
+    } catch {
+      continue;
+    }
+
+    if (selector === "#menu > ul > li") {
+      const ul = document.querySelector("#menu > ul") as HTMLElement | null;
+      if (ul) return ul;
+    } else if (selector === "#menu ul") {
+      const ul = document.querySelector("#menu ul") as HTMLElement | null;
+      if (ul) return ul;
+    } else {
+      const menu = document.getElementById("menu");
+      const ul =
+        (menu?.querySelector("ul") as HTMLElement | null) ??
+        (menu?.firstElementChild as HTMLElement | null);
+      if (ul) return ul;
+    }
+  }
+
+  console.warn(
+    "[BetterSEQTA+] Engage: could not find a menu list to inject the home button",
+  );
+  return null;
+}