refactor(web): sweep AGENTS.md TypeScript + Mantine rule violations (#1771)

Codebase-wide sweep bringing the web client into strict compliance with the AGENTS.md TypeScript and Mantine/React conventions: ~170 inline 2+-static-prop elements extracted to named .withProps() constants across ~77 files, the AGENTS.md rule wording tightened to match (static-prop boundary + Accordion/Transition/data-*/Box exemptions), a real ScreenStage Box->Flex layout regression fixed (direction: column) with a Storybook regression guard, and an App.tsx double-cast tightened. Closes #1762.

clients/web/src/components/elements/MethodBadge/MethodBadge.tsx

@@ -5,19 +5,17 @@ export interface MethodBadgeProps {
   method: string;
 }
 
+const MethodChip = Badge.withProps({
+  autoContrast: false,
+  bg: "var(--inspector-badge-method-bg)",
+  c: "var(--inspector-badge-method-fg)",
+});
+
 /**
  * Badge labelling a Protocol/Network entry's method. A neutral charcoal chip with
  * light text, driven by `--inspector-badge-method-*` so it stays legible (not a
  * washed-out pale fill) in dark mode. Shared by `ProtocolEntry` and `NetworkEntry`.
  */
 export function MethodBadge({ method }: MethodBadgeProps) {
-  return (
-    <Badge
-      autoContrast={false}
-      bg="var(--inspector-badge-method-bg)"
-      c="var(--inspector-badge-method-fg)"
-    >
-      {method}
-    </Badge>
-  );
+  return <MethodChip>{method}</MethodChip>;
 }