fix(rectification): render adoption carrier on deterministic choice path

frontend/tests/rectification-agentic-entry.test.ts

@@ -531,7 +531,7 @@ test("conversation and house board reuse the quiet overlay scrollbar", () => {
   assert.doesNotMatch(styles, /\.conversation:not\(\.is-empty\):not\(\.is-rectification\) \{[^}]*scrollbar-gutter/);
 });
 
-test("time-selection cards appear under the latest settled agent bubble only after offer-candidates", () => {
+test("time-selection cards use server adoption state and stay mutually exclusive with choice cards", () => {
   const messageLoop = chat.slice(
     chat.indexOf("{messages.map((message) => {"),
     chat.indexOf("{savedTime &&"),
@@ -543,7 +543,11 @@ test("time-selection cards appear under the latest settled agent bubble only aft
   assert.match(chat, /turnOfferedSelection/);
   assert.match(chat, /rectification-offer-candidates/);
   assert.match(chat, /showLiveChoiceCard = Boolean\(\s*choiceCard[\s\S]*answeredQuestionIds[\s\S]*!busy/);
-  assert.match(chat, /showSelectionCards = Boolean\(\s*candidateResult\?\.selectionAllowed[\s\S]*offeredSelectionOnce[\s\S]*!showLiveChoiceCard[\s\S]*!busy/);
+  assert.match(chat, /showSelectionCards = Boolean\(\s*candidateResult\?\.selectionAllowed[\s\S]*candidateResult\?\.canAdopt[\s\S]*!showLiveChoiceCard[\s\S]*!busy[\s\S]*!readonly/);
+  assert.doesNotMatch(
+    chat.slice(chat.indexOf("const showSelectionCards"), chat.indexOf("const selectionCardMessageKey")),
+    /offeredSelectionOnce/,
+  );
   assert.match(
     chat,
     /selectionCardMessageKey = showSelectionCards && latestSettledAssistant\s*\? latestSettledAssistant\.renderKey\s*: undefined/,