[KYUUBI #6619][FOLLOWUP] Do not log auth audit log for thrift http cookie auth

# 🔍 Description
## Issue References 🔗

Follow up for #6619, I found that, there are many duplicate auth audit logs for thrift http.

We shall only log when make authentication with auth handler, and skip it for cookie auth.
## Describe Your Solution 🔧

Please include a summary of the change and which issue is fixed. Please also include relevant motivation and context. List any dependencies that are required for this change.

## Types of changes 🔖

- [ ] Bugfix (non-breaking change which fixes an issue)
- [ ] New feature (non-breaking change which adds functionality)
- [ ] Breaking change (fix or feature that would cause existing functionality to change)

## Test Plan 🧪

#### Behavior Without This Pull Request ⚰️

#### Behavior With This Pull Request 🎉

#### Related Unit Tests

---

# Checklist 📝

- [ ] This patch was not authored or co-authored using [Generative Tooling](https://www.apache.org/legal/generative-tooling.html)

**Be nice. Be informative.**

Closes #6632 from turboFei/need_to_auth.

Closes #6619

3a25a3dd3 [Wang, Fei] do auth

Authored-by: Wang, Fei <fwang12@ebay.com>
Signed-off-by: Wang, Fei <fwang12@ebay.com>

kyuubi-server/src/main/scala/org/apache/kyuubi/server/http/ThriftHttpServlet.scala

@@ -80,6 +80,7 @@ class ThriftHttpServlet(
   override def doPost(request: HttpServletRequest, response: HttpServletResponse): Unit = {
     var clientUserName: String = null
     var requireNewCookie: Boolean = false
+    var doAuth: Boolean = false
     try {
       if (conf.get(KyuubiConf.FRONTEND_THRIFT_HTTP_XSRF_FILTER_ENABLED)) {
         val continueProcessing = doXsrfFilter(request, response)
@@ -111,6 +112,7 @@ class ThriftHttpServlet(
       // If the cookie based authentication is not enabled or the request does not have a valid
       // cookie, use authentication depending on the server setup.
       if (clientUserName == null) {
+        doAuth = true
         clientUserName = authenticate(request, response)
       }
 
@@ -143,7 +145,7 @@ class ThriftHttpServlet(
         error("Error: ", e)
         throw e
     } finally {
-      AuthenticationAuditLogger.audit(request, response)
+      if (doAuth) AuthenticationAuditLogger.audit(request, response)
       AuthenticationFilter.HTTP_CLIENT_USER_NAME.remove()
       AuthenticationFilter.HTTP_CLIENT_IP_ADDRESS.remove()
       AuthenticationFilter.HTTP_PROXY_HEADER_CLIENT_IP_ADDRESS.remove()
@@ -275,8 +277,10 @@ class ThriftHttpServlet(
 
   private def authenticate(request: HttpServletRequest, response: HttpServletResponse): String = {
     val authorization = request.getHeader(AUTHORIZATION_HEADER)
-    authenticationFilter.getMatchedHandler(authorization).map(
-      _.authenticate(request, response)).orNull
+    authenticationFilter.getMatchedHandler(authorization).map { authHandler =>
+      AuthenticationFilter.HTTP_AUTH_TYPE.set(authHandler.authScheme.toString)
+      authHandler.authenticate(request, response)
+    }.orNull
   }
 
   private def getDoAsQueryParam(queryString: String): String = {