How to propogate the ThreadContext or MDC traceId and spanId to the fallback thread pool in reselience4j

Question

Using the below property, I was able to propogate the ThreadContext to bulkhead pool.

resilience4j.thread-pool-bulkhead.instances.service.context-propagators[0]=com.config.MDCContextPropogater

But it seems that the fallback is executing on a different thread pool named: [pool-4-thread-1] and MDC or [TraceId,SpanId] is not propogating to it.

Is there a way to resolve this ?

 @Override
    @Bulkhead(name = service, type = Type.THREADPOOL, fallbackMethod = fallbackService)
    @TimeLimiter(name = service, fallbackMethod = fallbackService)
    @CircuitBreaker(name = service, fallbackMethod = fallbackService)
    public CompletableFuture<String> service(String request) {
        return CompletableFuture.completedFuture(process(request));
    }

    private String process(String request) {

        // [bulkhead-service-1] - thread pool - traceId, SpanId is present here
    }

    public CompletableFuture<String> fallbackService(String request, Exception e) {
    
        // [pool-4-thread-1] - thread pool - traceId, SpanId is not present here, as MDC context is not getting loaded here

       
    }

Is the fallback pool a fork-join-common-pool used by reslience 4j? If yes how to propogate MDC to it's threads.