Increase VectorEngine timeouts and add image UI

Add VectorEngine image generation config and raise request timeouts (env + scripts) from 180000 to 1000000ms. Introduce a reusable CreativeImageInputPanel component with tests and wire up mobile keyboard-focus helpers; update generation views and related tests (CustomWorldGenerationView, BarkBattle editor, Match3D, Puzzle flows). Improve API error handling / VectorEngine request guidance (packages/shared http.ts and docs), and apply multiple backend/frontend fixes for puzzle/match3d/prompt handling. Also include extensive docs and decision-log updates describing UI/UX decisions and verification steps.

server-rs/crates/api-server/src/edutainment_baby_object.rs

@@ -15,6 +15,7 @@ use serde_json::{Value, json};
 use crate::{
     api_response::json_success_body,
     character_visual_assets::try_apply_background_alpha_to_png,
+    config::DEFAULT_VECTOR_ENGINE_IMAGE_REQUEST_TIMEOUT_MS,
     http_error::AppError,
     openai_image_generation::{
         DownloadedOpenAiImage, OpenAiImageSettings, build_openai_image_http_client,
@@ -27,7 +28,6 @@ use crate::{
 const BABY_OBJECT_MATCH_PROVIDER: &str = "vector-engine-gpt-image-2";
 const BABY_OBJECT_MATCH_IMAGE_SIZE: &str = "1024x1024";
 const BABY_OBJECT_MATCH_BACKGROUND_IMAGE_SIZE: &str = "1536x1024";
-const BABY_OBJECT_MATCH_VECTOR_ENGINE_REQUEST_TIMEOUT_MS: u64 = 480_000;
 
 #[derive(Debug, Deserialize)]
 #[serde(rename_all = "camelCase")]
@@ -207,7 +207,7 @@ fn build_baby_object_match_negative_prompt() -> &'static str {
 fn with_baby_object_match_image_timeout(mut settings: OpenAiImageSettings) -> OpenAiImageSettings {
     settings.request_timeout_ms = settings
         .request_timeout_ms
-        .max(BABY_OBJECT_MATCH_VECTOR_ENGINE_REQUEST_TIMEOUT_MS);
+        .max(DEFAULT_VECTOR_ENGINE_IMAGE_REQUEST_TIMEOUT_MS);
     settings
 }
 
@@ -617,7 +617,7 @@ mod tests {
 
         assert_eq!(
             settings.request_timeout_ms,
-            BABY_OBJECT_MATCH_VECTOR_ENGINE_REQUEST_TIMEOUT_MS
+            DEFAULT_VECTOR_ENGINE_IMAGE_REQUEST_TIMEOUT_MS
         );
     }