fix(rectification): keep one delivery and adopt with the birth date

Accept and GET now decide with the same birth snapshot as the answer, so an under-age probe cannot flip can_adopt. The exit skips a second write when this reply already delivered. The card stays without an adopt button when adoption is not allowed, and a refusal shows the Chinese sentence.

frontend/tests/database-segment-opening.test.ts

@@ -81,7 +81,7 @@ test("segment opening PostgreSQL owns stable domain, full original checks and on
     assert.equal(fixture.psql(`select count(*) from public.agentic_rectification_conversation_focuses where case_id='${caseId}'`), "0");
     const dossier = await loadV9CaseDossier(service, userId, caseId);
     assert.equal(dossier.case.status, "closed");
-    const publicView = dossierResponse(dossier, [], { status: "current", requiresSkillAdoption: false } as never);
+    const publicView = dossierResponse(dossier, [], { status: "current", requiresSkillAdoption: false } as never, { birthDate: "1900-06-15" });
     assert.equal(publicView.current_question, null);
     assert.equal(publicView.choice_card, null);
     assert.equal(publicView.step_state.headline, "盘型一致，不用校正");