fix(extension-api): unify NodeEntityId/WidgetEntityId brand and tighten World stub

Resolves ~40 pre-existing typecheck failures on the foundation branch
caused by divergent entity-ID brand definitions:

- src/world/entityIds.ts brands as string + brand
- src/extension-api/{node,widget}.ts brands as number + brand

Both are now unified by re-exporting the world-layer brand from the
public API surface (string is canonical because Phase A entity IDs are
formatted like 'node:<graphUuid>:<localId>').

Also:
- World.getComponent / setComponent / removeComponent / entitiesWith are
  now properly generic over <TData, TEntity>, so call sites get typed
  data back instead of unknown.
- WidgetComponentSchema/Display/Value/Serialize/Container in
  src/world/widgets/widgetComponents.ts get real data shapes
  (type/options/label/hidden/disabled/value/serialize/widgetIds)
  instead of opaque 'object'.
- getMode() casts the int return to NodeMode union.
- Hook result is typed as unknown so the runtime defensive Promise +
  setupReturn checks don't trip TS2358 / TS1345.
- dynamicPrompts.v2.ts: widget.getValue<string>() (method-generic does
  not exist) → widget.getValue() as string.

Result: 'pnpm typecheck' is now clean on ext-api/i-foundation.

src/extension-api/node.ts

@@ -23,11 +23,14 @@ import type { WidgetHandle, WidgetOptions } from './widget'
 
 /**
  * Branded entity ID for nodes. Prevents mixing node IDs with widget IDs
- * at compile time. The underlying value is always `number`.
+ * at compile time. Re-exported from the world layer so the entire codebase
+ * shares a single brand. The underlying value is `string` in Phase A
+ * (e.g. `node:<graphUuid>:<localId>`).
  *
  * @stability stable
  */
-export type NodeEntityId = number & { readonly __brand: 'NodeEntityId' }
+import type { NodeEntityId } from '@/world/entityIds'
+export type { NodeEntityId }
 
 // ─── Geometry ────────────────────────────────────────────────────────────────
 

src/extension-api/widget.ts

@@ -21,11 +21,13 @@ import type { AsyncHandler, Handler, Unsubscribe } from './events'
 
 /**
  * Branded entity ID for widgets. Prevents mixing widget IDs with node IDs
- * at compile time. The underlying value is always `number`.
+ * at compile time. Re-exported from the world layer so the entire codebase
+ * shares a single brand. The underlying value is `string` in Phase A.
  *
  * @stability stable
  */
-export type WidgetEntityId = number & { readonly __brand: 'WidgetEntityId' }
+import type { WidgetEntityId } from '@/world/entityIds'
+export type { WidgetEntityId }
 
 // ─── Widget value ────────────────────────────────────────────────────────────
 

src/extensions/core/dynamicPrompts.v2.ts

@@ -16,7 +16,7 @@ defineNodeExtension({
       if (widget.getOption('dynamicPrompts')) {
         widget.on('beforeSerialize', (e) => {
           if (e.context === 'prompt') {
-            const value = widget.getValue<string>()
+            const value = widget.getValue() as string
             e.setSerializedValue(
               typeof value === 'string' ? processDynamicPrompt(value) : value
             )

src/services/extension-api-service.ts

@@ -42,6 +42,7 @@ import { defineComponentKey } from '@/world/componentKey'
 
 import type {
   NodeHandle,
+  NodeMode,
   SlotInfo,
   SlotEntityId as PublicSlotEntityId,
   Point,
@@ -287,7 +288,7 @@ function createNodeHandle(nodeId: NodeEntityId): NodeHandle {
       return world.getComponent(nodeId, NodeVisualKey)?.title ?? ''
     },
     getMode() {
-      return world.getComponent(nodeId, ExecutionKey)?.mode ?? 0
+      return (world.getComponent(nodeId, ExecutionKey)?.mode ?? 0) as NodeMode
     },
 
     getProperty<T = unknown>(key: string): T | undefined {
@@ -552,7 +553,7 @@ export function mountExtensionsForNode(nodeEntityId: NodeEntityId): void {
       _currentScope = record
       pauseTracking()
       try {
-        const result = hook(createNodeHandle(nodeEntityId))
+        const result: unknown = hook(createNodeHandle(nodeEntityId))
         if (result instanceof Promise) {
           // Async setup is not supported (D10c) — catch to prevent unhandled rejection
           result.catch((err) => {

src/world/widgets/widgetComponents.ts

@@ -2,9 +2,29 @@
 // Tests mock this module via vi.mock('@/world/widgets/widgetComponents').
 
 import { defineComponentKey } from '../componentKey'
+import type { NodeEntityId, WidgetEntityId } from '../entityIds'
 
-export const WidgetComponentContainer = defineComponentKey<object, unknown>('WidgetComponentContainer')
-export const WidgetComponentDisplay = defineComponentKey<object, unknown>('WidgetComponentDisplay')
-export const WidgetComponentSchema = defineComponentKey<object, unknown>('WidgetComponentSchema')
-export const WidgetComponentSerialize = defineComponentKey<object, unknown>('WidgetComponentSerialize')
-export const WidgetComponentValue = defineComponentKey<object, unknown>('WidgetComponentValue')
+interface WidgetContainerData {
+  widgetIds: WidgetEntityId[]
+}
+interface WidgetDisplayData {
+  label?: string
+  hidden?: boolean
+  disabled?: boolean
+}
+interface WidgetSchemaData {
+  type?: string
+  options?: Record<string, unknown>
+}
+interface WidgetSerializeData {
+  serialize?: boolean
+}
+interface WidgetValueData {
+  value?: unknown
+}
+
+export const WidgetComponentContainer = defineComponentKey<WidgetContainerData, NodeEntityId>('WidgetComponentContainer')
+export const WidgetComponentDisplay = defineComponentKey<WidgetDisplayData, WidgetEntityId>('WidgetComponentDisplay')
+export const WidgetComponentSchema = defineComponentKey<WidgetSchemaData, WidgetEntityId>('WidgetComponentSchema')
+export const WidgetComponentSerialize = defineComponentKey<WidgetSerializeData, WidgetEntityId>('WidgetComponentSerialize')
+export const WidgetComponentValue = defineComponentKey<WidgetValueData, WidgetEntityId>('WidgetComponentValue')

src/world/worldInstance.ts

@@ -1,11 +1,26 @@
 // Phase A stub — replaced by real ECS world when PR #11939 lands.
 // Tests mock this module via vi.mock('@/world/worldInstance').
 
+import type { ComponentKey } from './componentKey'
+import type { EntityId } from './entityIds'
+
 export interface World {
-  getComponent(entityId: unknown, key: unknown): unknown
-  setComponent(entityId: unknown, key: unknown, data: unknown): void
-  removeComponent(entityId: unknown, key: unknown): void
-  entitiesWith(key: unknown): unknown[]
+  getComponent<TData, TEntity extends EntityId>(
+    entityId: TEntity,
+    key: ComponentKey<TData, TEntity>
+  ): TData | undefined
+  setComponent<TData, TEntity extends EntityId>(
+    entityId: TEntity,
+    key: ComponentKey<TData, TEntity>,
+    data: TData
+  ): void
+  removeComponent<TData, TEntity extends EntityId>(
+    entityId: TEntity,
+    key: ComponentKey<TData, TEntity>
+  ): void
+  entitiesWith<TData, TEntity extends EntityId>(
+    key: ComponentKey<TData, TEntity>
+  ): TEntity[]
 }
 
 export function getWorld(): World {