How to add mocked S3Client to spring context on integration tests

Question

So basically I have a S3StorageService class that needs a S3Client:

@RequiredArgsConstructor
@Service
public class S3StorageService implements StorageService<S3FileUploadResult> {
    private final S3Client client;

// ...
}

and I have a SongServiceImpl class:

@RequiredArgsConstructor
@Service
public class SongServiceImpl implements SongService {
    private final StorageService<?> storageService;

    @Transactional
    @Override
    public Song uploadSong(UploadSongDTO dto) {
        // ...
        storageService.upload(dto.file());
    }
}

and I have a SongController class:

@RequiredArgsConstructor
@RequestMapping("/song")
@RestController
public class SongController {
    private final SongService songService;

    @PostMapping("/upload")
    public ResponseEntity<Song> upload(@Valid UploadSongDTO dto) {
        return ResponseEntity.ok(songService.uploadSong(dto));
    }
}

so i want to write integration tests for this SongController#upload, so i need to somehow inject a mocked S3Client into spring context so S3StorageService can use this mocked s3 instead of a real one, here is what i tried:

   static S3MockContainer s3Mock = new S3MockContainer("latest");

    @BeforeEach
    void setUp() {
        final String endpoint = s3Mock.getHttpsEndpoint();
        final S3Configuration serviceConfig = S3Configuration.builder()
                .pathStyleAccessEnabled(true)
                .build();
        final SdkHttpClient httpClient = UrlConnectionHttpClient.builder()
                .buildWithDefaults(AttributeMap.builder()
                        .put(TRUST_ALL_CERTIFICATES, Boolean.TRUE)
                        .build());
        final S3Client s3Client = S3Client.builder() // somehow inject this into S3StorageService
                .region(Region.of("auto"))
                .endpointOverride(URI.create(endpoint))
                .serviceConfiguration(serviceConfig)
                .httpClient(httpClient)
                .build();

        applicationContext.registerBean(S3Client.class, () -> s3Client); // does not work. `Parameter 0 of constructor in me.approximations.music.services.storage.impl.S3StorageService required a bean of type 'software.amazon.awssdk.services.s3.S3Client' that could not be found.`
    }

Already described above.