Implement API setup with configuration management and startup tasks

- Add `Cargo.toml` for API with dependencies.
- Create `config.rs` for managing application settings.
- Implement logging and server settings in `config.rs`.
- Add `main.rs` to initialize the application and handle database connections.
- Introduce `task` module with startup tasks, including database migrations.
- Update `.gitignore` to exclude `config.yaml` and remove `.gitkeep`.

apps/api/Cargo.toml

@@ -0,0 +1,19 @@
+[package]
+name = "yet-another-nginx-proxy-manager"
+version = "0.1.0"
+edition = "2024"
+
+[dependencies]
+database = { path = "../../public/database" }
+migration = { path = "../../public/migration" }
+
+axum = { version = "0.8.7", features = ["form", "http1", "json", "matched-path", "original-uri", "query", "tokio", "tower-log", "tracing", "macros"]}
+chrono = { version = "0.4.42", features = ["clock", "std", "oldtime", "wasmbind", "serde"] }
+config = { version = "0.15.19", features = ["toml", "json", "yaml", "ini", "ron", "json5", "convert-case", "async"] }
+tokio = { version = "1", features = ["fs", "io-util", "io-std", "macros", "net", "parking_lot", "process", "rt", "rt-multi-thread", "signal", "sync", "time", "tracing"] }
+tower = { version = "0.5.2", features = ["tokio", "tracing"] }
+tower-http = { version = "0.6.6" }
+tracing = { version = "0.1.41", features = ["std", "attributes"] }
+tracing-subscriber = { version = "0.3.20", features = ["smallvec", "fmt", "ansi", "tracing-log", "std", "chrono", "json", "serde", "serde_json", "time", "tracing"] }
+serde_json = { version = "1.0.145", features = ["std"] }
+serde = { version = "1.0.228", features = ["std", "derive"] }