feat: Rust port of Claude Code CLI

Crates:
- api: Anthropic Messages API client with SSE streaming
- tools: Claude-compatible tool implementations (Bash, Read, Write, Edit, Glob, Grep + extended suite)
- runtime: conversation loop, session persistence, permissions, system prompt builder
- rusty-claude-cli: terminal UI with markdown rendering, syntax highlighting, spinners
- commands: subcommand definitions
- compat-harness: upstream TS parity verification

All crates pass cargo fmt/clippy/test.

rust/crates/api/Cargo.toml

@@ -0,0 +1,15 @@
+[package]
+name = "api"
+version.workspace = true
+edition.workspace = true
+license.workspace = true
+publish.workspace = true
+
+[dependencies]
+reqwest = { version = "0.12", default-features = false, features = ["json", "rustls-tls"] }
+serde = { version = "1", features = ["derive"] }
+serde_json = "1"
+tokio = { version = "1", features = ["io-util", "macros", "net", "rt-multi-thread", "time"] }
+
+[lints]
+workspace = true