fix(tui): default alternate screen to always

[echobt]

Summary

Interactive TUI launch now enters the alternate screen by default (alternate_screen always), matching a Codex-style full viewport. The host terminal is taken over on start instead of remaining inline.

Welcome splash is unchanged from #17: Welcome to Cortex, the coding agent CLI plus the version / command legend. No fake > cortex prompt or cwd lines. Composer dual-hairline and caret-before-placeholder are unchanged.

Opt out to stay inline:

• [tui] alternate_screen = false in config
• cortex --no-alternate-screen on the CLI
• --alternate-screen still forces the alternate buffer when config is false

Test plan

• cargo fmt --all -- --check
• ./scripts/clippy.sh (local: -p cortex-cli; workspace gate in CI)
• cargo test -p cortex-cli --lib -- test_cli_alternate_screen plus engine alternate_screen tests
• TUI / snapshot tests for every surface this PR touches (TUI checks job was already green; lock proof still asserts no fake > cortex)
• cargo audit (or note a documented .cargo/audit.toml exception) — CI Security Audit was green on the previous run

Attestation (required)

I attest that:

• Security reviewed — auth, exec/sandbox, path traversal, network egress, and secret handling in this diff were reviewed. No secrets, tokens, or keyring dumps are in the change.
• Product-facing errors — user-visible failures use Cortex product copy. API-down paths say The coding service is temporarily unavailable. No raw provider, SDK, or transport names.
• TUI verified — every TUI surface touched in this PR was exercised (build + headless snapshot / ratatui-style test). CI TUI checks were green.
• Tests added — unit tests cover the new logic; TUI changes include a snapshot or buffer assertion. No mocks that report success.
• No secrets — no API keys, WorkOS secrets, R2/AWS credentials, or .env files are included.

Risk

Low. Default TUI terminal mode only. No auth, exec policy, sandbox, or API-contract changes. Users who want the previous inline layout set [tui] alternate_screen = false or --no-alternate-screen.