Remove unreachable TUI helpers and duplicate state

[shiny-code-bot]

Finish Line

Unused speculative agent-install APIs and duplicate unread App state are removed while preserving any helper proven load-bearing by the authoritative Every Code source.

Current Status

The agent-install status API has no consumer in either current TUI flow; authoritative Every Code retains only the macOS formula helper for its agent editor. App.arg0_paths and App.strict_config are unread duplicate copies of values already threaded through configuration paths.

Acceptance Criteria

• Remove speculative install-status and path-probing APIs with no consumer.
• Retain or remove the macOS formula helper based on the account/agent-editor restoration dependency, without broad dead-code allowances.
• Remove duplicate unread App fields and initializer plumbing.
• Existing focused TUI tests pass.
• Exact Bazel Clippy clears this cleanup cluster.

Relationships

• Third implementation stage of Restore TUI reachability for exact Bazel Clippy #685.

Open Questions

• Keep the macOS formula helper only if the planned authoritative agent-editor port consumes it in the same reviewable sequence.