RestTemplateEurekaHttpClient not closing HttpClient on shutdown

Spring Cloud 2021.0.0
Spring Boot 2.6.8

Bug Description:
RestTemplateEurekaHttpClient is not closing HttpClient on shutdown. This leads to TCP CLOSE_WAIT connections to eureka server.

EurekaClient will shutdown when an exception occurs on an http request, but not shutdown HttpClient.

This bug is related to https://github.com/spring-cloud/spring-cloud-netflix/blob/27ac3379f6b391ccd605d212512f15c439825ecb/spring-cloud-netflix-eureka-client/src/main/java/org/springframework/cloud/netflix/eureka/http/RestTemplateEurekaHttpClient.java#L203

In case of exception here:
https://github.com/Netflix/eureka/blob/ed0da19ca1c049c87e3dbf75b6015c1861d5c2d0/eureka-client/src/main/java/com/netflix/discovery/shared/transport/decorator/RedirectingEurekaHttpClient.java#L96
new HttpClient will be created without closing the existing one - this causes CLOSE_WAIT connections

This supplier creates new CloseableHttpClient for every call to https://github.com/spring-cloud/spring-cloud-netflix/blob/27ac3379f6b391ccd605d212512f15c439825ecb/spring-cloud-netflix-eureka-client/src/main/java/org/springframework/cloud/netflix/eureka/http/RestTemplateTransportClientFactory.java#L103

public class DefaultEurekaClientHttpRequestFactorySupplier implements EurekaClientHttpRequestFactorySupplier {

	@Override
	public ClientHttpRequestFactory get(SSLContext sslContext, @Nullable HostnameVerifier hostnameVerifier) {
		HttpClientBuilder httpClientBuilder = HttpClients.custom();
		if (sslContext != null) {
			httpClientBuilder = httpClientBuilder.setSSLContext(sslContext);
		}
		if (hostnameVerifier != null) {
			httpClientBuilder = httpClientBuilder.setSSLHostnameVerifier(hostnameVerifier);
		}
		CloseableHttpClient httpClient = httpClientBuilder.build();
		HttpComponentsClientHttpRequestFactory requestFactory = new HttpComponentsClientHttpRequestFactory();
		requestFactory.setHttpClient(httpClient);
		return requestFactory;
	}

}

so in case of shutdown, currentEurekaClient shutdown don't closes connections:
https://github.com/spring-cloud/spring-cloud-netflix/blob/27ac3379f6b391ccd605d212512f15c439825ecb/spring-cloud-netflix-eureka-client/src/main/java/org/springframework/cloud/netflix/eureka/http/RestTemplateEurekaHttpClient.java#L203

possible solution will be trying to close the HttpClient:
shutdown could be

public void shutdown() {
        Optional.of(unwrapRequestFactoryIfNecessary(restTemplate.getRequestFactory()))
                .filter(HttpComponentsClientHttpRequestFactory.class::isInstance)
                .map(HttpComponentsClientHttpRequestFactory.class::cast)
                .ifPresent(requestFactory-> {
                    try {
                        requestFactory.destroy();
                    } catch (Exception e) {
                    }
                });
    }

unwrapRequestFactoryIfNecessary
https://github.com/spring-projects/spring-boot/blob/47516b50c39bd6ea924a1f6720ce6d4a71088651/spring-boot-project/spring-boot/src/main/java/org/springframework/boot/web/client/RestTemplateBuilder.java#L746

spring-projects/spring-boot#31075

As you can see process open files increases over time until GC occurred

We can also create EurekaClientHttpRequestFactorySupplier which return the same ClientHttpRequestFactory, but it not a stable solution since we can't control eureka client code, maybe in case of exceptions connections not closes (hence not returns to PoolingHttpClientConnectionManager) - this can lead to no available connections in pool. In that case, restart is required

Original Issue:
https://github.com/spring-cloud/spring-cloud-netflix/issues/4062