### Elasticsearch Version

main

### Installed Plugins

_No response_

### Java Version

_bundled_

### OS Version

MacOS

### Problem Description

Currently, transform state persistence failures are being retried with a constant interval (`60s`).
This is different to how other types of errors are retried (exponential backoff).
We should implement exponential backoff for state persistence failures too.

### Steps to Reproduce

n/a

### Logs (if relevant)

_No response_
x-pack/plugin/transform/src/main/java/org/elasticsearch/xpack/transform/transforms/ClientTransformIndexer.java
searchRequest.source().pointInTimeBuilder(null);
                    ClientHelper.executeWithHeadersAsync(
                        transformConfig.getHeaders(),
                        ClientHelper.TRANSFORM_ORIGIN,
                        client,
                        SearchAction.INSTANCE,
                        searchRequest,
                        listener
                    );
                    return;
                }
                if (unwrappedException instanceof IndexNotFoundException && pit != null) {
                    /*
                     * gh#81252 pit API search request can fail if indices get deleted (by ILM)
                     * fall-back to normal search, the pit gets re-created (with an updated set of indices) on the next run
                     *
                     * Note: Due to BWC this needs to be kept until CCS support for < 8.1 is dropped
                     */
                    namedPits.remove(name);
                    searchRequest.source().pointInTimeBuilder(null);
                    ClientHelper.executeWithHeadersAsync(
                        transformConfig.getHeaders(),
                        ClientHelper.TRANSFORM_ORIGIN,
                        client,
                        SearchAction.INSTANCE,
                        searchRequest,
                        listener
                    );
                    return;
                }