feat: add Rust reverse proxy with JSON logging

- Axum-based API server with Unix socket and TCP support
- Custom tracing formatters for Railway-compatible JSON logs
- SvelteKit hooks and Vite plugin for unified logging
- Justfile updated for concurrent dev workflow with hl log viewer

Cargo.toml

@@ -0,0 +1,20 @@
+[package]
+name = "api"
+version = "0.1.0"
+edition = "2024"
+
+[dependencies]
+axum = "0.8.8"
+clap = { version = "4.5.54", features = ["derive", "env"] }
+nu-ansi-term = "0.50.3"
+reqwest = { version = "0.13", features = ["charset", "json"], default-features = false }
+serde = { version = "1.0.228", features = ["derive"] }
+serde_json = "1.0.148"
+time = { version = "0.3.44", features = ["formatting", "macros"] }
+tokio = { version = "1.49.0", features = ["full"] }
+tokio-util = { version = "0.7.18", features = ["io"] }
+tower = "0.5"
+tower-http = { version = "0.6.8", features = ["trace", "cors"] }
+tracing = "0.1.44"
+tracing-subscriber = { version = "0.3.22", features = ["env-filter", "json"] }
+ulid = { version = "1", features = ["serde"] }