feat: expand InitializationState with explicit lifecycle state machine

[dgenio]

Summary

Addresses #1691 — Phase 1: expand the InitializationState enum with an explicit lifecycle state machine and add centralized transition validation.

Problem

The current ServerSession lifecycle management uses a simple three-state enum (NotInitialized, Initializing, Initialized) with direct state assignment. This makes it difficult to reason about session lifecycle, provides no protection against invalid transitions, and lacks visibility into shutdown states. Stateless sessions were handled by jumping directly to Initialized, conflating two conceptually different modes.

Solution

Expanded InitializationState enum

• Stateless — sessions that skip the initialization handshake (previously mapped to Initialized)
• Closing — session is shutting down, entered during __aexit__
• Closed — terminal state after shutdown completes

An Error state for unrecoverable failures is planned for Phase 2 of #1691.

Centralized transition validation

• _VALID_TRANSITIONS dict — maps each state to its valid target states, documenting the state machine in one place
• _transition_state() method — validates transitions and raises RuntimeError on invalid ones, with debug logging
• Re-initialization (Initialized → Initializing) is explicitly allowed for backward compatibility
• NotInitialized → Initialized is allowed to handle cases where the client sends an InitializedNotification without a prior InitializeRequest round-trip

Concurrency documentation

• Class-level docstring on ServerSession documents the single-consumer concurrency model: incoming messages are processed sequentially by _receive_loop, so _transition_state() needs no external synchronization
• _transition_state() docstring explains why cooperative scheduling makes the method safe without locks

New properties

• initialization_state — read-only access to current state
• is_initialized — returns True for both Initialized and Stateless (replaces direct comparisons)

__aexit__ override

• Transitions through Closing → Closed on session exit
• Gracefully handles edge cases (already closing/closed)

Updated handlers

• _received_request and _received_notification now use _transition_state() instead of direct assignment
• _received_notification guards against redundant InitializedNotification in stateless mode

Tests

20 new tests in tests/server/test_session_lifecycle.py covering:

• Enum completeness and value uniqueness
• Transition table correctness (all states have entries, Closed is terminal)
• Valid and invalid state transitions via _transition_state()
• is_initialized property for all states
• __aexit__ lifecycle transitions (including already-closing and already-closed edge cases)
• Full client/server handshake integration test

[dgenio]

Hi — I'm the author of this PR. Just checking in after @maxisbey's feedback about waiting for transport spec finalization.

I designed this as a non-breaking Phase 1 — it only expands the existing enum and adds validated transitions without changing the public API surface. The Stateless, Closing, and Closed states are internal and the is_initialized property is additive. If the transport spec changes require additional states (e.g., Resuming, Reconnecting), those can be added to the transition table without reworking anything here.

That said, I completely understand if you'd prefer to wait until the transport discussions linked above converge before merging lifecycle changes. Happy to keep this PR updated in the meantime — it applies cleanly to current main and I can rebase as needed.

Would love to hear if Phase 1 is acceptable as an incremental step, or if you'd rather hold off entirely. Thanks!