fix(demo): relative asset paths in bitcoin-ui/fedimint-ui shells

The shells are served at / in their containers but under /app/<id>/ in
the public demo, where absolute /tailwind.css and /assets/... 404 — the
Bitcoin UI rendered unstyled with a giant unconstrained SVG. Relative
paths resolve correctly in both contexts.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

docker/bitcoin-ui/index.html

@@ -7,7 +7,9 @@
     <meta http-equiv="Pragma" content="no-cache">
     <meta http-equiv="Expires" content="0">
     <title id="pageTitle">Bitcoin Node - Archipelago</title>
-    <link rel="stylesheet" href="/tailwind.css">
+    <!-- Relative: the shell is served at / in the container but under
+         /app/bitcoin-ui/ in the public demo — absolute paths 404 there. -->
+    <link rel="stylesheet" href="tailwind.css">
     <style>
         * {
             margin: 0;
@@ -339,7 +341,7 @@
                     <div class="logo-gradient-border">
                         <img
                             id="implLogo"
-                            src="/assets/img/app-icons/bitcoin-knots.webp"
+                            src="assets/img/app-icons/bitcoin-knots.webp"
                             alt="Bitcoin Node"
                             class="w-16 h-16"
                             style="object-fit: contain;"
@@ -984,8 +986,8 @@
                 ? 'Enhanced Bitcoin node implementation'
                 : 'Reference Bitcoin node implementation';
             const icon = isKnots
-                ? '/assets/img/app-icons/bitcoin-knots.webp'
-                : '/assets/img/app-icons/bitcoin-core.svg';
+                ? 'assets/img/app-icons/bitcoin-knots.webp'
+                : 'assets/img/app-icons/bitcoin-core.svg';
             const pageTitle = document.getElementById('pageTitle');
             const implName = document.getElementById('implName');
             const implTagline = document.getElementById('implTagline');