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

database_manager/Cargo.toml

@@ -11,7 +11,7 @@ clap_utils = { workspace = true }
 environment = { workspace = true }
 hex = { workspace = true }
 serde = { workspace = true }
-slog = { workspace = true }
 store = { workspace = true }
 strum = { workspace = true }
+tracing = { workspace = true }
 types = { workspace = true }