fix(rectification): keep choice stems visible and align overlay adopt with the engine

Walkthrough polish: fail-closed empty D9 prompts, stop asserting the next question is on screen, vary same-domain collect copy, switch to reverse-verify after adopt, and let coverage route interview without blocking can_adopt.

Co-authored-by: Cursor <cursoragent@cursor.com>

frontend/src/lib/rectification-agentic/core/rectification-decision.ts

@@ -205,10 +205,10 @@ function deliveryCapability(input: {
   holdout: HoldoutValidationStatus;
   engineCeiling: EngineCapabilityCeiling;
   confirmationAllowed: boolean;
-  coverageComplete: boolean;
+  trainingGateOpen: boolean;
 }): DeliveryCapability {
   const locallySelectable = input.separation.ranked.length > 0
-    && input.coverageComplete
+    && input.trainingGateOpen
     && input.stopClass?.kind !== "keep_collecting";
   return {
     canAdopt: locallySelectable && input.engineCeiling.acceptanceAllowed,
@@ -246,7 +246,7 @@ export function decideRectification(input: DecideRectificationInput): Rectificat
     holdout,
     engineCeiling: input.engineCeiling,
     confirmationAllowed,
-    coverageComplete: input.methodCoverageAll && input.trainingGateOpen !== false,
+    trainingGateOpen: input.trainingGateOpen !== false,
   });
 
   if (input.snapshotCurrent === false) {