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

testing/web3signer_tests/src/lib.rs

@@ -25,7 +25,6 @@ mod tests {
     use initialized_validators::{
         load_pem_certificate, load_pkcs12_identity, InitializedValidators,
     };
-    use logging::test_logger;
     use parking_lot::Mutex;
     use reqwest::Client;
     use serde::Serialize;
@@ -316,7 +315,6 @@ mod tests {
             using_web3signer: bool,
             spec: Arc<ChainSpec>,
         ) -> Self {
-            let log = test_logger();
             let validator_dir = TempDir::new().unwrap();
 
             let config = initialized_validators::Config::default();
@@ -325,7 +323,6 @@ mod tests {
                 validator_definitions,
                 validator_dir.path().into(),
                 config.clone(),
-                log.clone(),
             )
             .await
             .unwrap();
@@ -340,8 +337,12 @@ mod tests {
             );
             let (runtime_shutdown, exit) = async_channel::bounded(1);
             let (shutdown_tx, _) = futures::channel::mpsc::channel(1);
-            let executor =
-                TaskExecutor::new(Arc::downgrade(&runtime), exit, log.clone(), shutdown_tx);
+            let executor = TaskExecutor::new(
+                Arc::downgrade(&runtime),
+                exit,
+                shutdown_tx,
+                "test".to_string(),
+            );
 
             let slashing_db_path = validator_dir.path().join(SLASHING_PROTECTION_FILENAME);
             let slashing_protection = SlashingDatabase::open_or_create(&slashing_db_path).unwrap();
@@ -365,7 +366,6 @@ mod tests {
                 slot_clock,
                 &config,
                 executor,
-                log.clone(),
             );
 
             Self {