fix(desktop): align CLI readiness with agent PATH

[etinpres]

Summary

• Resolve CLI login probes from the same augmented PATH used by the managed-agent child process.
• Prevent an older ambient PATH wrapper from falsely marking a healthy CLI as logged out and forcing the agent into setup mode.
• Add a regression test and document the readiness invariant.

Problem

Managed-agent readiness resolved the CLI with the desktop process ambient PATH, then executed the login probe with the augmented child PATH. Those two operations could select different executables.

For example, an older wrapper earlier on the desktop ambient PATH can fail codex login status, while the managed-agent child PATH correctly prefers an authenticated Codex CLI installed under NVM. Buzz then reports a false login requirement and starts the otherwise healthy agent in setup mode.

Implementation

• Build the augmented child PATH before resolving the login-probe executable.
• On Unix, search that PATH in order and require an executable file.
• Retain the existing resolver as the fallback for explicit paths and platform-specific command handling.
• Add resolve_probe_command_prefers_augmented_child_path to pin the precedence.

Related work

No exact open issue or PR was found for this login-readiness mismatch.

• Onboarding: ACP adapter install fails silently when a broken Node shadows Buzz's managed Node in the login shell #3451 covers a different PATH shadowing case during adapter installation.
• fix(desktop): spawn agents with the configured relay URL, not the canonical form #5200 covers the separate configured-relay versus canonical-runtime-key problem discovered during the same end-to-end investigation. That relay fix is intentionally not duplicated here.

Validation

• just ci — passed
• cargo test --manifest-path desktop/src-tauri/Cargo.toml managed_agents::readiness — 54 passed, 0 failed
• Desktop frontend tests — 4,535 passed, 0 failed
• Tauri workspace tests — 2,271 passed, 0 failed, 14 ignored
• Mobile tests — 1,261 passed
• Desktop and web production builds passed

No UI changes.