Quarkus OIDC Session Cookie not deleted in case of 401 unauthorized
### Describe the bug

In case the verification of the oidc session cookie fails (for instance because the id token is malformed, expired, ...), then the server response with an http 401. however, the server is not deleting the session cookie. hence all subsequent requests also fail with 401 without the change for the user to recover. Only deleting the session cookie or waiting for it to expire is possible.

### Expected behavior

If the server response with http 401, then the server also deletes the q_session cookie.

### Actual behavior

If the server response with http 401, then the (invalid) q_session cookie is not deleted automatically.

### How to Reproduce?

1) Login into your web application
2) manipulate the session cookie
3) perform another activity in the web application

### 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

2.16.3.Final

### Build tool (ie. output of `mvnw --version` or `gradlew --version`)

_No response_

### Additional information

_No response_
diff --git a/extensions/oidc/runtime/src/main/java/io/quarkus/oidc/runtime/CodeAuthenticationMechanism.java b/extensions/oidc/runtime/src/main/java/io/quarkus/oidc/runtime/CodeAuthenticationMechanism.java
index 55396274e51..0dde01e5b97 100644
--- a/extensions/oidc/runtime/src/main/java/io/quarkus/oidc/runtime/CodeAuthenticationMechanism.java
+++ b/extensions/oidc/runtime/src/main/java/io/quarkus/oidc/runtime/CodeAuthenticationMechanism.java
@@ -321,8 +321,13 @@ public Uni<? extends SecurityIdentity> apply(Throwable t) {
 
                                             if (!expired) {
                                                 LOG.errorf("ID token verification failure: %s", t.getCause());
-                                                return Uni.createFrom()
-                                                        .failure(new AuthenticationCompletionException(t.getCause()));
+                                                return removeSessionCookie(context, configContext.oidcConfig)
+                                                        .replaceWith(Uni.createFrom()
+                                                                .failure(t
+                                                                        .getCause() instanceof AuthenticationCompletionException
+                                                                                ? t.getCause()
+                                                                                : new AuthenticationCompletionException(
+                                                                                        t.getCause())));
                                             }
                                             // Token has expired, try to refresh
                                             if (session.getRefreshToken() == null) {
diff --git a/integration-tests/oidc-code-flow/src/test/java/io/quarkus/it/keycloak/CodeFlowTest.java b/integration-tests/oidc-code-flow/src/test/java/io/quarkus/it/keycloak/CodeFlowTest.java
index abe8b76675f..a67cd4eb3f9 100644
--- a/integration-tests/oidc-code-flow/src/test/java/io/quarkus/it/keycloak/CodeFlowTest.java
+++ b/integration-tests/oidc-code-flow/src/test/java/io/quarkus/it/keycloak/CodeFlowTest.java
@@ -564,6 +564,22 @@ public void testIdTokenInjection() throws IOException {
             page = webClient.getPage("http://localhost:8081/web-app");
 
             assertEquals("alice", page.getBody().asNormalizedText());
+
+            Cookie sessionCookie = getSessionCookie(webClient, null);
+            assertNotNull(sessionCookie);
+            webClient.getCookieManager().clearCookies();
+            webClient.getCookieManager().addCookie(new Cookie(sessionCookie.getDomain(), sessionCookie.getName(),
+                    "1|2|3"));
+            sessionCookie = getSessionCookie(webClient, null);
+            assertEquals("1|2|3", sessionCookie.getValue());
+
+            try {
+                webClient.getPage("http://localhost:8081/web-app");
+                fail("401 status error is expected");
+            } catch (FailingHttpStatusCodeException ex) {
+                assertEquals(401, ex.getStatusCode());
+                assertNull(getSessionCookie(webClient, null));
+            }
             webClient.getCookieManager().clearCookies();
         }
     }
['integration-tests/oidc-code-flow/src/test/java/io/quarkus/it/keycloak/CodeFlowTest.java', 'extensions/oidc/runtime/src/main/java/io/quarkus/oidc/runtime/CodeAuthenticationMechanism.java']