Add generationStatus and match3d/runtime fixes

Introduce persistent generationStatus to work summaries (puzzle & match3d) and propagate generation recovery rules across docs and frontend/backends so "generating" is restored from server-side work summary rather than ephemeral front-end notices. Update API server image/asset handling (improve match3d material sheet green/alpha decontamination and promote generatedItemAssets background fields) and add runtime improvements: alpha-based hotspot hit-testing, tray insertion/three-match animation behavior, and session re-read on client-side VectorEngine timeouts/lock-screen interruptions. Many docs, tests and related frontend modules updated/added to reflect these contract and behavior changes.

server-rs/crates/api-server/src/puzzle/mappers.rs

@@ -278,10 +278,31 @@ pub(super) fn map_puzzle_result_preview_finding_response(
     }
 }
 
+fn resolve_puzzle_work_generation_status(item: &PuzzleWorkProfileRecord) -> Option<String> {
+    item.levels
+        .iter()
+        .map(|level| level.generation_status.trim())
+        .find(|status| *status == "generating")
+        .or_else(|| {
+            item.levels
+                .iter()
+                .map(|level| level.generation_status.trim())
+                .find(|status| *status == "ready")
+        })
+        .or_else(|| {
+            item.levels
+                .iter()
+                .map(|level| level.generation_status.trim())
+                .find(|status| !status.is_empty())
+        })
+        .map(str::to_string)
+}
+
 pub(super) fn map_puzzle_work_summary_response(
     state: &AppState,
     item: PuzzleWorkProfileRecord,
 ) -> PuzzleWorkSummaryResponse {
+    let generation_status = resolve_puzzle_work_generation_status(&item);
     let author = resolve_work_author_by_user_id(
         state,
         &item.owner_user_id,
@@ -316,6 +337,7 @@ pub(super) fn map_puzzle_work_summary_response(
             .saturating_div(2)
             .saturating_sub(item.point_incentive_claimed_points),
         publish_ready: item.publish_ready,
+        generation_status,
         levels: Vec::new(),
     }
 }