Pitch

`crates/tui/src/tui/app.rs::App` is now ~200+ public fields, many of which group naturally:

• `onboarding_*` (4 fields)
• `approval_*` (3 fields)
• `composer_*` (5+ fields)
• `runtime_turn_*` (3 fields)
• `subagent_*` (4 fields)
• `transcript_*` (5 fields)
• ...

Each cluster could be its own struct (`OnboardingState`, `ApprovalCache`, `ComposerState`, `TurnState`, `SubagentTracker`, `TranscriptViewport`) with focused methods. `App` becomes a thin top-level container of these. Easier to read, easier to test, easier to refactor later.

Acceptance

• No behavior change — every existing call site continues to compile and pass.
• App's field count drops by at least 30%.
• At least 3 new sub-state structs land with their own `#[cfg(test)]` coverage.
• Standard verification gates pass.

Why now

Acquisition-readiness: a future maintainer reading `App` for the first time should see structure, not a flat 200-field god struct. This refactor pays for itself within a few PRs.