Repository: quarkusio/quarkus
Issue: WebSocket auth on VertxCurrentContext not working

### Describe the bug

Hello. In my comman we use auth on WebSocket class by this hack

```
@RouteFilter(401)
void addAuthHeader(RoutingContext rc) {
    try {
        if (rc.request().headers().get("Sec-WebSocket-Protocol") != null) {
            String token = "Bearer " + rc.request().headers().get("Sec-WebSocket-Protocol").split(", ")[1];
            rc.request().headers().add("Authorization", token);
        }
    } finally {
        rc.next();
    }
}
```

We make ws request such this

```
const ws = new WebSocket(`ws://localhost:8080/ws`, ["access_token", "token"]);
```

And WebSoket class such as

```
@ServerEndpoint(
        value = "/api/v1/notification-socket/{userId}",
        decoders = SocketMessageDecoder.class,
        encoders = SocketMessageEncoder.class
)
@Authenticated
public class WS {
    // ......
}
```

Last version when it works is **2.12.3.Final**
It works by changes in this commit - [Add proper identity propagation to WebSockets](https://github.com/quarkusio/quarkus/pull/20157/commits/d6a421a5a2e433e6ea4aa966fc66842bebae40fd) - File WebsocketCoreRecorder

After update to version 2.13 and higher it work only then used property 
`quarkus.vertx.customize-arc-context=false`
In version 2.13 added changes from this commit [CDI context propagation improvements for the reactive stack](https://github.com/quarkusio/quarkus/pull/27443). 
Now where is two CurrentContext implementations - ThreadLocalCurrentContext (ws auth works) and VertxCurrentContext (ws auth not work)

This code from WebsocketCoreRecorder
```
boolean required = !requestContext.isActive();
if (required) {
    requestContext.activate();
    Principal p = session.getUserPrincipal();
    if (p instanceof WebSocketPrincipal) {
        CurrentIdentityAssociation current = this.getCurrentIdentityAssociation();
        if (current != null) {
            current.setIdentity(((WebSocketPrincipal)p).getSecurityIdentity());
        }
    }
}
```
When uses ThreadLocalCurrentContext  - requestContext.isActive() is false, and principal added in context
When uses VertxCurrentContext - requestContext.isActive() is always true, and user don`t added on context

Maybe fix this place, or create fix VertxCurrentContext? 
Thank you for your job)

### Expected behavior

_No response_

### Actual behavior

_No response_

### How to Reproduce?

_No response_

### Output of `uname -a` or `ver`

_No response_

### Output of `java -version`

_No response_

### GraalVM version (if different from Java)

_No response_

### Quarkus version or git rev

2.13+

### Build tool (ie. output of `mvnw --version` or `gradlew --version`)

_No response_

### Additional information

_No response_

Changed files:
extensions/websockets/client/runtime/src/main/java/io/quarkus/websockets/client/runtime/WebsocketCoreRecorder.java

diff --git a/extensions/websockets/client/runtime/src/main/java/io/quarkus/websockets/client/runtime/WebsocketCoreRecorder.java b/extensions/websockets/client/runtime/src/main/java/io/quarkus/websockets/client/runtime/WebsocketCoreRecorder.java
index ca321461c59..670656f1a0a 100644
--- a/extensions/websockets/client/runtime/src/main/java/io/quarkus/websockets/client/runtime/WebsocketCoreRecorder.java
+++ b/extensions/websockets/client/runtime/src/main/java/io/quarkus/websockets/client/runtime/WebsocketCoreRecorder.java
@@ -169,12 +169,12 @@ public T call(C context, UndertowSession session) throws Exception {
                                 boolean required = !requestContext.isActive();
                                 if (required) {
                                     requestContext.activate();
-                                    Principal p = session.getUserPrincipal();
-                                    if (p instanceof WebSocketPrincipal) {
-                                        var current = getCurrentIdentityAssociation();
-                                        if (current != null) {
-                                            current.setIdentity(((WebSocketPrincipal) p).getSecurityIdentity());
-                                        }
+                                }
+                                Principal p = session.getUserPrincipal();
+                                if (p instanceof WebSocketPrincipal) {
+                                    var current = getCurrentIdentityAssociation();
+                                    if (current != null) {
+                                        current.setIdentity(((WebSocketPrincipal) p).getSecurityIdentity());
                                     }
                                 }
                                 try {