chore(lint): biome cleanup across services — format, sort imports, drop unused

- discord-gateway: 74 lint errors -> 0 (format, import sorting, unused
  imports/vars, dead breath var)
- backend: format + sort imports (11 warnings left: noExplicitAny)
- frontend: remove unused imports, drop dead breathing var, fix
  useExhaustiveDependencies (scroll keyed on messages), a11y biome-ignore
  for drag surface + stopPropagation container (mouse-only gestures)
- remaining warnings are false positives: index keys on static lists,
  <img> in static export (next/image unsupported), noExplicitAny

tsc --noEmit clean on all 3 services; vitest green (60+36).

services/frontend/src/components/chatbot/chatbot-canvas.tsx

@@ -33,7 +33,14 @@ export function ChatbotCanvas() {
     ctx.clearRect(0, 0, w, h);
 
     // Background circle
-    const gradient = ctx.createRadialGradient(w / 2, h / 2 - 10, 10, w / 2, h / 2, 80);
+    const gradient = ctx.createRadialGradient(
+      w / 2,
+      h / 2 - 10,
+      10,
+      w / 2,
+      h / 2,
+      80,
+    );
     gradient.addColorStop(0, "oklch(0.62 0.17 215 / 0.8)");
     gradient.addColorStop(0.6, "oklch(0.12 0.02 245 / 0.9)");
     gradient.addColorStop(1, "oklch(0.07 0.015 250 / 1)");
@@ -112,11 +119,6 @@ export function ChatbotCanvas() {
       ctx.arc(w / 2, 75, 6, 0.1, Math.PI - 0.1);
       ctx.stroke();
     }
-
-    // Breathing animation — subtle canvas shift
-    const breath = Math.sin(Date.now() / 1000) * 1.5;
-    // Applied via CSS transform on container instead
-
   }, [expression]);
 
   return (