refactor(app): extract navigation and conversation action dispatch

[Andiveli]

Problem / requested outcome

src/app/inputs.rs still executes navigation and conversation AppAction variants directly, leaving terminal routing coordination mixed with action effects.

Motivating example

The preceding input refactor slices already delegate modal/picker-viewer and lifecycle/settings action families. The remaining navigation and conversation family should follow the same boundary.

Expected behavior

Extract the remaining action execution into a cohesive handler, keep inputs.rs responsible for terminal orchestration and routing coordination, preserve exhaustive AppAction handling and exact behavior, and add focused tests.

Current limitation

dispatch_action contains both input-dispatch coordination and navigation/conversation side effects, which keeps the SRP chain incomplete.

Evidence

Parent PR #351: refactor/rust-input-lifecycle-dispatch. Child work targets refactor/rust-input-lifecycle-dispatch. Verification is intentionally limited to git diff --check; Cargo, formatter, and target commands are not run.

Scope

This is a refactor only; no user-facing behavior should change.