feat: default OAuth config for claude.com, merge UI polish rendering

CLAUDE.md

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+# CLAUDE.md
+
+This file provides guidance to Claude Code (claude.ai/code) when working with code in this repository.
+
+## Detected stack
+- Languages: Rust.
+- Frameworks: none detected from the supported starter markers.
+
+## Verification
+- Run Rust verification from `rust/`: `cargo fmt`, `cargo clippy --workspace --all-targets -- -D warnings`, `cargo test --workspace`
+- `src/` and `tests/` are both present; update both surfaces together when behavior changes.
+
+## Repository shape
+- `rust/` contains the Rust workspace and active CLI/runtime implementation.
+- `src/` contains source files that should stay consistent with generated guidance and tests.
+- `tests/` contains validation surfaces that should be reviewed alongside code changes.
+
+## Working agreement
+- Prefer small, reviewable changes and keep generated bootstrap files aligned with actual repo workflows.
+- Keep shared defaults in `.claude.json`; reserve `.claude/settings.local.json` for machine-local overrides.
+- Do not overwrite existing `CLAUDE.md` content automatically; update it intentionally when repo workflows change.