在这个问题上浪费了几个小时之后，我找到了解决这个问题的方法。
最简单和最不具侵入性的方法是在ExampleExtensionTest上使用@EnabledIfSystemProperty(name = "some-property")注解。
代码如下：

import org.junit.jupiter.api.Test;
import org.junit.jupiter.api.extension.ExtendWith;
import org.junit.jupiter.engine.descriptor.JupiterEngineDescriptor;
import org.junit.platform.testkit.engine.EngineExecutionResults;
import org.junit.platform.testkit.engine.EngineTestKit;
import org.slf4j.Logger;
import org.slf4j.LoggerFactory;

import java.io.IOException;
import java.nio.file.Path;

import static org.junit.platform.engine.discovery.DiscoverySelectors.selectClass;

public class ExtensionTest
{

    private final Logger logger = LoggerFactory.getLogger(ExtensionTest.class);

    @BeforeAll
    public static void beforeAll()
    {
        System.setProperty("my-property", "true");
    }

    @AfterAll
    public static void afterAll()
    {
        System.clearProperty("my-property");
    }

    @Test
    public void extensionShouldGenerateReport() throws IOException
    {

        Path reportPath = Path.of("build/tmp/example-recorded-test");
        logger.info("Configured report path: {}", reportPath);

        EngineTestKit.engine(JupiterEngineDescriptor.ENGINE_ID)
                     .selectors(selectClass(ExtensionTest.ExampleExtensionTest.class))
                     .execute()
                     .containerEvents()
                     .assertStatistics(stats -> stats.started(1).succeeded(1));

        // Assert all files were generated.
        assertThat(reportPath.toFile().exists()).isTrue();
        assertThat(reportPath.resolve("index.html").toFile().exists()).isTrue();
        assertThat(reportPath.resolve("metadata.json").toFile().exists()).isTrue();

    }

    @ExtendWith(MyExtension.class)
    @EnabledIfSystemProperty(named = "my-property", matches = "true")
    static class ExampleExtensionTest
    {
        @MyAnnotation(reportPath = "build/tmp/example-recorded-test")
        public void test()
        {
            return; // noop.
        }
    }

}

这将导致测试被排除在全局运行之外，但当通过EngineTestKit以编程方式调用它时，它仍然工作。