Best way to use Websocket with Spring Boot and Vuejs

I try to use Websocket with spring boot backend (as an API) and Vuejs frontend.

I take a simple use case to expose my question. Some users are logged on my website, and there is a messaging feature. User A send a message to User B. User B is actually logged, and I want to notify User B that a new message is arrived.

I see 3 ways to do it with websockets :

1 - When User A send message, an Axios post is call to the API for saving message, and, if the Axios response is success, I call something like

this.stompClient.send("/app/foo", JSON.stringify(bar), {})

2 - When User A send message, I only call something like

this.stompClient.send("/app/foo", JSON.stringify(bar), {})

and it's my controller's method (annotated with @MessageMapping("/xxxx") @SendTo("/topic/yyyy")) that call facade, service, dao to first, save message, then return message to subscribers

3 - I keep my actuals controllers, facade, services and DAO, and juste add when save is successfull something like :

@Autowired SimpMessagingTemplate webSocket; 
...
@GetMapping("/send-message")
public ResponseEntity sendMessage(@AuthenticationPrincipal User user, ....) {
    service.saveMessage(....);
    webSocket.convertAndSend("/ws/message-from", message);

without a new controller contains @MessageMapping("/xxxx") @SendTo("/topic/yyyy"). User B is just subscibed to "/ws/message-from"

Could you help me.

In the 3 way there is a good method ?

Thanks you.