feat(ads): carry the banner scroll position across navigation

Per the owner's idea: instead of moving the banner out of the per-screen header
(which would change its position), remember the banner's "life stage" and resume
it on the next screen. The engine already keeps the message + rotation timing;
this adds the scroll offset:

- bannerEngine tracks the in-flight scroll (target, duration, start). On attach,
  if a scroll is still running, it computes the current offset and calls the new
  host's resumeScroll(fromTx, toPx, remaining) — the view jumps to the carried
  offset and continues to the end over the remaining time, instead of restarting
  at the left.
- A finished scroll is left at its end; the rotator's own loop then takes over.

Verified: spot-checked in the browser (a long message at offset -785 resumes at
-788 on the next screen, not 0) and unit-tested (attach mid-scroll calls
resumeScroll with a partial offset and the remaining duration).

ui/src/lib/bannerEngine.ts

@@ -10,15 +10,20 @@ let rotator: Rotator | null = null;
 let mounted: BannerHost | null = null;
 let current = '';
 let key = '';
+// The in-flight horizontal scroll of the current message, so a view mounted by navigation can
+// resume it from the same offset instead of restarting at the left. Null when not scrolling.
+let activeScroll: { toPx: number; dur: number; start: number } | null = null;
 
-// proxy is the rotator's host: it records the current message (so a freshly-mounted view can
-// resync to it) and forwards every effect to the currently-attached DOM host, if any.
+// proxy is the rotator's host: it records the current message + scroll (so a freshly-mounted view
+// can resume them) and forwards every effect to the currently-attached DOM host, if any.
 const proxy: BannerHost = {
   show(md) {
     current = md;
+    activeScroll = null;
     mounted?.show(md);
   },
   resetScroll() {
+    activeScroll = null;
     mounted?.resetScroll();
   },
   hide(durationMs) {
@@ -28,8 +33,12 @@ const proxy: BannerHost = {
     return mounted?.overflowPx() ?? 0;
   },
   scrollTo(toPx, durationMs) {
+    activeScroll = { toPx, dur: durationMs, start: Date.now() };
     mounted?.scrollTo(toPx, durationMs);
   },
+  resumeScroll(fromTx, toPx, durationMs) {
+    mounted?.resumeScroll(fromTx, toPx, durationMs);
+  },
 };
 
 // bannerKey identifies a campaigns+timings set so configureBanner restarts the cycle only on a
@@ -70,6 +79,16 @@ export function bannerCurrent(): string {
  */
 export function attachBannerHost(host: BannerHost): void {
   mounted = host;
+  // Resume the current message's scroll from where it had reached, so navigation does not restart
+  // a long message at the left. Only while a scroll is still in flight; a finished scroll is left
+  // at its end and the rotator's own loop takes over.
+  if (activeScroll) {
+    const elapsed = Date.now() - activeScroll.start;
+    if (elapsed < activeScroll.dur) {
+      const progress = elapsed / activeScroll.dur;
+      host.resumeScroll(-activeScroll.toPx * progress, activeScroll.toPx, activeScroll.dur - elapsed);
+    }
+  }
 }
 
 /**