proxy: change is cold start to enum (#6948)

## Problem

Actually it's good idea to distinguish between cases when it's a cold
start, but we took the compute from the pool

## Summary of changes

Updated to enum.

proxy/src/context.rs

@@ -9,7 +9,7 @@ use tracing::{field::display, info_span, Span};
 use uuid::Uuid;
 
 use crate::{
-    console::messages::MetricsAuxInfo,
+    console::messages::{ColdStartInfo, MetricsAuxInfo},
     error::ErrorKind,
     metrics::{LatencyTimer, ENDPOINT_ERRORS_BY_KIND, ERROR_BY_KIND},
     BranchId, DbName, EndpointId, ProjectId, RoleName,
@@ -42,7 +42,7 @@ pub struct RequestMonitoring {
     error_kind: Option<ErrorKind>,
     pub(crate) auth_method: Option<AuthMethod>,
     success: bool,
-    is_cold_start: Option<bool>,
+    cold_start_info: Option<ColdStartInfo>,
 
     // extra
     // This sender is here to keep the request monitoring channel open while requests are taking place.
@@ -91,7 +91,7 @@ impl RequestMonitoring {
             error_kind: None,
             auth_method: None,
             success: false,
-            is_cold_start: None,
+            cold_start_info: None,
 
             sender: LOG_CHAN.get().and_then(|tx| tx.upgrade()),
             latency_timer: LatencyTimer::new(protocol),
@@ -115,7 +115,7 @@ impl RequestMonitoring {
         self.set_endpoint_id(x.endpoint_id);
         self.branch = Some(x.branch_id);
         self.project = Some(x.project_id);
-        self.is_cold_start = x.is_cold_start;
+        self.cold_start_info = x.cold_start_info;
     }
 
     pub fn set_project_id(&mut self, project_id: ProjectId) {