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/Cargo.toml

@@ -29,9 +29,9 @@ reqwest = { workspace = true }
 sensitive_url = { workspace = true }
 serde = { workspace = true }
 slashing_protection = { workspace = true }
-slog = { workspace = true }
 slot_clock = { workspace = true }
 tokio = { workspace = true }
+tracing = { workspace = true }
 types  = { workspace = true }
 validator_http_api = { workspace = true }
 validator_http_metrics = { workspace = true }