Integrate tracing (#6339)

Tracing Integration
- [reference](5bbf1859e9/projects/project-ideas.md (L297))


  - [x] replace slog & log with tracing throughout the codebase
- [x] implement custom crit log
- [x] make relevant changes in the formatter
- [x] replace sloggers
- [x] re-write SSE logging components

cc: @macladson @eserilev

validator_client/src/check_synced.rs

@@ -0,0 +1,25 @@
+use crate::beacon_node_fallback::CandidateError;
+use eth2::{types::Slot, BeaconNodeHttpClient};
+use tracing::warn;
+
+pub async fn check_node_health(
+    beacon_node: &BeaconNodeHttpClient,
+) -> Result<(Slot, bool, bool), CandidateError> {
+    let resp = match beacon_node.get_node_syncing().await {
+        Ok(resp) => resp,
+        Err(e) => {
+            warn!(
+                error = %e,
+                "Unable connect to beacon node"
+            );
+
+            return Err(CandidateError::Offline);
+        }
+    };
+
+    Ok((
+        resp.data.head_slot,
+        resp.data.is_optimistic,
+        resp.data.el_offline,
+    ))
+}