feat(proxy): Log latency after connect to compute (#11048)

## Problem
To measure latency accurate we should associate the testodrome role
within a latency data

## Summary of changes
Add latency logging to associate different roles within a latency.

Relates to the #22486

proxy/src/context/mod.rs

@@ -17,7 +17,8 @@ use crate::control_plane::messages::{ColdStartInfo, MetricsAuxInfo};
 use crate::error::ErrorKind;
 use crate::intern::{BranchIdInt, ProjectIdInt};
 use crate::metrics::{
-    ConnectOutcome, InvalidEndpointsGroup, LatencyTimer, Metrics, Protocol, Waiting,
+    ConnectOutcome, InvalidEndpointsGroup, LatencyAccumulated, LatencyTimer, Metrics, Protocol,
+    Waiting,
 };
 use crate::protocol2::{ConnectionInfo, ConnectionInfoExtra};
 use crate::types::{DbName, EndpointId, RoleName};
@@ -346,6 +347,14 @@ impl RequestContext {
         }
     }
 
+    pub(crate) fn get_proxy_latency(&self) -> LatencyAccumulated {
+        self.0
+            .try_lock()
+            .expect("should not deadlock")
+            .latency_timer
+            .accumulated()
+    }
+
     pub(crate) fn success(&self) {
         self.0
             .try_lock()