feat(persons): updatePerson persists personType from DTO

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

backend/src/test/java/org/raddatz/familienarchiv/service/PersonServiceTest.java

@@ -182,6 +182,23 @@ class PersonServiceTest {
                 .isEqualTo(400);
     }
 
+    // ─── updatePerson (personType) ───────────────────────────────────────────
+
+    @Test
+    void updatePerson_persistsPersonType() {
+        UUID id = UUID.randomUUID();
+        Person person = Person.builder().id(id).firstName("Anna").lastName("Alt").personType(PersonType.PERSON).build();
+        when(personRepository.findById(id)).thenReturn(Optional.of(person));
+        when(personRepository.save(any())).thenAnswer(inv -> inv.getArgument(0));
+
+        PersonUpdateDTO dto = new PersonUpdateDTO();
+        dto.setFirstName("Anna"); dto.setLastName("Alt"); dto.setPersonType(PersonType.INSTITUTION);
+
+        Person result = personService.updatePerson(id, dto);
+
+        assertThat(result.getPersonType()).isEqualTo(PersonType.INSTITUTION);
+    }
+
     // ─── updatePerson (alias) ─────────────────────────────────────────────────
 
     @Test