fix(claude): give spawned CLI a working PATH; prefer configured binary

[sam-powers]

What & why

When Quill runs as a packaged macOS .app launched from Finder, launchd hands it a minimal PATH (/usr/bin:/bin:/usr/sbin:/sbin) that lacks Node. Since claude is a #!/usr/bin/env node script, the spawned process died with env: node: No such file or directory — @claude replies and full-document review silently failed for installed users. (It never reproduced under tauri dev from a terminal, which is why it went unnoticed.)

This ports three related backend behavior specs (docs/to-improve/01–03) into the public repo, adapted to this repo's conventions rather than pasted from the fork.

Changes (src-tauri/src/lib.rs)

• Give the spawned CLI a working PATH. New pure, unit-tested build_child_path assembles the child's PATH — the resolved binary's own dir first (its sibling node lives there for nvm/Homebrew layouts), then the login-shell PATH, the inherited PATH, and well-known fallbacks (nvm newest-first, ~/.local/bin, Homebrew, system dirs) — de-duplicated preserving first occurrence. Wired into spawn_claude_resume via .env("PATH", …) (alongside the existing .env_remove("ANTHROPIC_API_KEY"), untouched).
• Prefer the user's configured binary. Reordered resolve_claude_binary: which → login shell → hardcoded dir scan last. Previously the scan ran before the shell and could pick a stale global install that emits a deprecated request shape and 400s ("thinking.type.enabled" is not supported…). The scan is now a last-resort fallback, never a preemption.
• Use an interactive login shell. -ilc instead of -lc, because toolchain PATH lines (nvm/fnm/Homebrew/Volta) commonly live in .zshrc/.bashrc, which a non-interactive login shell doesn't source. Binary resolution takes the last non-empty stdout line (banner-proof); the child-PATH read prints $PATH behind a unique sentinel so rc/profile banners can't clobber it. Shell reads are factored into login_shell_stdout so the two callers don't duplicate the invocation.

Testing

• cargo test — 39 pass, including four new build_child_path tests: includes the binary's own dir; claude dir comes first; de-dups preserving first occurrence; well-known dirs present when login + inherited PATH are both absent (the packaged-.app worst case).
• cargo clippy -- -D warnings and cargo fmt --check — clean.
• Frontend suite (255 tests) green via pre-commit hook.
• Manual, out of automated scope: the real .app-from-Finder spawn path can't be reconstructed in cargo test — verify by building the .app, launching from Finder, and confirming an @claude reply streams instead of env: node: No such file or directory.

Notes

• No frontend routes affected (Rust-backend-only), so browser testing is not applicable.
• Does not touch the user's stale claude install — only the preference order.
• First of a multi-group port of docs/to-improve/ (this PR = Group 1, specs 01–03). The full spec set is vendored here for provenance; Groups 2–5 follow in separate PRs.

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