SDK Clients are Closeable and documented as thread safe but don't provide an isClosed() method

[markjschreiber]

Describe the bug

Because SDK clients are Closeable they might be auto-closed if placed in a "try with resources" block. The SDK documentation encourages re-use of clients and advertises them as thread safe. This can mean another thread or a try with resources block might close a client without you realizing. Unfortunately you cannot check if the client is still open because there is no isClosed() method.

Expected Behavior

Ability to determine if a client is closed.

Current Behavior

No ability to determine if a client is closed (without making an API call).

Reproduction Steps

S3Client client;

// on another thread
try (client = S3Client.builder().build()) {
   // do some things
}

// back on the main thread the client has been auto closed but you don't know and cannot tell
client.headBucketRequest(...);  // will fail

### Possible Solution

* presence of an `isClosed()` method
* Or, to make it truly safe, future calls to a closed client could automatically re-establish a connection pool internally

### Additional Information/Context

_No response_

### AWS Java SDK version used

2.25.51

### JDK version used

OpenJDK Runtime Environment Corretto-17.0.11.9.1 (build 17.0.11+9-LTS)

### Operating System and version

Mac OS 14.4.1 (23E224)

[debora-ito]

@markjschreiber feature request acknowledged, added to the backlog.