Update Match3D/image-generation docs & code

Adds/updates documentation, assets and implementation for Match3D and puzzle image generation workflows. Key changes: decision logs and pitfalls updated to prefer VectorEngine Gemini for Match3D material sheets and to require edits (multipart) for 1:1 container reference images; guidance added for when to use APIMart vs VectorEngine. .env.example clarified APIMart/Responses config. Many new public assets and PPT visuals added. Code changes across frontend and backend: updated shared contracts, server-rs match3d/puzzle/image-generation handlers, VectorEngine/OpenAI image generation clients, and multiple React components/tests to handle UI/background/container image signing, edits workflow, and puzzle UI background resolution. Added src/services/puzzle-runtime/puzzleUiBackgroundSource.ts and related test updates. Includes notes about multipart HTTP/1.1 requirement and test/verification commands in docs.

src/components/platform-entry/PlatformEntryFlowShellImpl.tsx

@@ -642,6 +642,7 @@ function mapPublicWorkDetailToMatch3DWork(
     backgroundImageSrc: entry.backgroundImageSrc ?? null,
     backgroundImageObjectKey: entry.backgroundImageObjectKey ?? null,
     generatedBackgroundAsset:
+      entry.generatedBackgroundAsset ??
       entry.generatedItemAssets
         ?.map((asset) => asset.backgroundAsset ?? null)
         .find(Boolean) ?? null,
@@ -744,6 +745,32 @@ function resolveMatch3DRuntimeGeneratedItemAssets(
     : normalizeMatch3DGeneratedItemAssetsForRuntime(profileAssets);
 }
 
+function resolveMatch3DRuntimeGeneratedBackgroundAsset(
+  run: Match3DRunSnapshot | null,
+  profile: Match3DWorkProfile | null,
+  publicWorkDetail: PlatformPublicGalleryCard | null,
+) {
+  const runProfileId = run?.profileId?.trim() ?? '';
+  const profileBackground = profile?.generatedBackgroundAsset ?? null;
+  const publicBackground =
+    publicWorkDetail && isMatch3DGalleryEntry(publicWorkDetail)
+      ? (publicWorkDetail.generatedBackgroundAsset ?? null)
+      : null;
+
+  if (runProfileId && profile?.profileId === runProfileId) {
+    return profileBackground ?? publicBackground;
+  }
+  if (
+    runProfileId &&
+    publicWorkDetail &&
+    isMatch3DGalleryEntry(publicWorkDetail) &&
+    publicWorkDetail.profileId === runProfileId
+  ) {
+    return publicBackground ?? profileBackground;
+  }
+  return profileBackground ?? publicBackground;
+}
+
 function resolveActiveMatch3DRuntimeProfile(
   run: Match3DRunSnapshot | null,
   runtimeProfile: Match3DWorkProfile | null,
@@ -8911,6 +8938,11 @@ export function PlatformEntryFlowShellImpl({
             activeMatch3DRuntimeProfile,
             activeEntry,
           )}
+          generatedBackgroundAsset={resolveMatch3DRuntimeGeneratedBackgroundAsset(
+            match3dRun,
+            activeMatch3DRuntimeProfile,
+            activeEntry,
+          )}
           backgroundImageSrc={resolveMatch3DRuntimeBackgroundImageSrc(
             match3dRun,
             activeMatch3DRuntimeProfile,
@@ -10985,6 +11017,11 @@ export function PlatformEntryFlowShellImpl({
                   activeMatch3DRuntimeProfile,
                   selectedPublicWorkDetail,
                 )}
+                generatedBackgroundAsset={resolveMatch3DRuntimeGeneratedBackgroundAsset(
+                  match3dRun,
+                  activeMatch3DRuntimeProfile,
+                  selectedPublicWorkDetail,
+                )}
                 backgroundImageSrc={resolveMatch3DRuntimeBackgroundImageSrc(
                   match3dRun,
                   activeMatch3DRuntimeProfile,