Similarly to https://github.com/elastic/elasticsearch/pull/97873 but for request handlers: let's stop passing around strings and looking these things up by name on each request when we could just pass around the `Executor` itself.
server/src/main/java/org/elasticsearch/action/support/HandledTransportAction.java
Request,
    Response> {
    protected HandledTransportAction(
        String actionName,
        TransportService transportService,
        ActionFilters actionFilters,
        Writeable.Reader<Request> requestReader
    ) {
        this(actionName, true, transportService, actionFilters, requestReader);
    }
    protected HandledTransportAction(
        String actionName,
        TransportService transportService,
        ActionFilters actionFilters,
        Writeable.Reader<Request> requestReader,
        Executor executor
    ) {
        this(actionName, true, transportService, actionFilters, requestReader, executor);
    }
    /**
     * Temporary for serverless compatibility. TODO remove.
     */
    protected HandledTransportAction(
        String actionName,
        TransportService transportService,
        ActionFilters actionFilters,
        Writeable.Reader<Request> requestReader,
        String executor
    ) {
        this(actionName, true, transportService, actionFilters, requestReader, transportService.getThreadPool().executor(executor));