FluxOperations.java

  public Mono<ServerResponse> createOrUpdateBulkMapping(ServerRequest serverRequest) {

	Flux<RequestObjects> requestFlux = serverRequest.bodyToFlux(RequestObjects.class);
	List<RequestObjects> createdList = new ArrayList<>();
	List<RequestObjects> updatedList = new ArrayList<>();
	return requestFlux.flatMap(entry -> {
	    
	    Flux<MyObjects> existingMapping = myRepository
		    .findByIdAndName(entry.getId(), entry.getName());

	    return existingMapping.map(optional -> {
		  if (optional != null) {
		    
		    updatedList.add(entry);
		    MyObject model = MyObjectMapper.updateModel(entry,
			    optional);
		    myRepository.save(model);
		    return model;
		} else {
		    
		    createdList.add(entry);
		    MyObject model = MyObjectMapper.convertToModel(entry);
		    myRepository.save(model)
		    return model;
		}
	 });

	}).then(ServerResponse.ok().body(Mono.just("Bulk Create/Update is successful").log(), String.class));
}

//This successfully executes but doesn't save or update any objects in repository

you cannot do this updatedList.add(entry); or createdList.add(entry);
because, updatedList can take only MyObjects type, but entry is RequestObjects type

and it will not work because you are breaking the chain. myRepository.save(model); is outside the chain. you should include it inside your chain. see the solution i have given against you question on stackoverflow and please copy the whole solution and then try to edit after pasting.
https://stackoverflow.com/questions/61362483/implementing-upsert-functionality-for-object-flux#61381724