feat(examples): migrate tap_battle session lifecycle to SessionManager

[salazarsebas]

Background

tap_battle demonstrates passkey authentication (secp256r1) combined with scoped gameplay sessions. Its session lifecycle is implemented via the pre-1.1.0 SessionBuilder pattern in src/auth.rs.

cougr-core 1.1.0 introduces session::SessionManager as the beta-standard API for session approval, execution, renewal, and status queries. That API is demonstrated in session_arena. Maintaining two session patterns without explicit classification risks directing integrators toward a deprecated approach.

Objective

Migrate tap_battle to SessionManager while preserving its public contract API and passkey authentication flow.

In scope

1. Replace custom session state management with SessionManager (approve, execute_action, renew, status).
2. Retain existing public function signatures (register_passkey, authenticate, tap, use_power_up, and related entrypoints).
3. Preserve the passkey flow: Secp256r1Storage, verify_secp256r1, and associated registration logic.
4. Upgrade to cougr-core = "1.1.0".
5. Update README.md to document the session lifecycle under SessionManager and reference session_arena as the minimal session example.
6. Add test coverage for session expiry and fallback behavior, consistent with the pattern in session_arena.
7. Add a cross-reference in session_arena/README.md to tap_battle for passkey-specific integration.

Out of scope

• Changes to passkey registration or verification primitives.
• Frontend or wallet integration work.

Definition of done

• All existing tap_battle tests pass.
• stellar contract build succeeds.
• Gameplay paths route session operations exclusively through SessionManager; direct SessionStorage manipulation is removed from gameplay code.
• README.md includes an updated session lifecycle description.

Dependencies

• Should follow or run in parallel with canonical session_arena compliance work (see the canonical 1.1.0 reference examples issue).

Supersedes

• feat(examples): migrate tap_battle to SessionManager #211

[Kappa16]

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[Oluwasuyi-Oluwatimilehin-Daniel]

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[madisonsc52-del]

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