chore(proxy): demote a ton of logs for successful connection attempts (#9803)

See https://github.com/neondatabase/cloud/issues/14378

In collaboration with @cloneable and @awarus, we sifted through logs and
simply demoted some logs to debug. This is not at all finished and there
are more logs to review, but we ran out of time in the session we
organised. In any slightly more nuanced cases, we didn't touch the log,
instead leaving a TODO comment.

proxy/src/context/mod.rs

@@ -8,7 +8,7 @@ use pq_proto::StartupMessageParams;
 use smol_str::SmolStr;
 use tokio::sync::mpsc;
 use tracing::field::display;
-use tracing::{debug, info, info_span, Span};
+use tracing::{debug, info_span, Span};
 use try_lock::TryLock;
 use uuid::Uuid;
 
@@ -122,6 +122,7 @@ impl RequestMonitoring {
         protocol: Protocol,
         region: &'static str,
     ) -> Self {
+        // TODO: be careful with long lived spans
         let span = info_span!(
             "connect_request",
             %protocol,
@@ -384,6 +385,10 @@ impl RequestMonitoringInner {
         } else {
             ConnectOutcome::Failed
         };
+
+        // TODO: get rid of entirely/refactor
+        // check for false positives
+        // AND false negatives
         if let Some(rejected) = self.rejected {
             let ep = self
                 .endpoint_id
@@ -391,7 +396,7 @@ impl RequestMonitoringInner {
                 .map(|x| x.as_str())
                 .unwrap_or_default();
             // This makes sense only if cache is disabled
-            info!(
+            debug!(
                 ?outcome,
                 ?rejected,
                 ?ep,