feat(http): trigger lifespan events when using mount_http() (adopted from #311, closes #256)

[K4bain]

Adopted from #311 (original patch by @Emeralden) — rebased onto current main and verified. Closes #256.

Why this is needed

mount_http() starts the StreamableHTTP session manager lazily on the first request. Consequences:

• The MCP session manager lifecycle runs completely outside the app's lifespan — lifespan-initialised resources (DB pools, caches) are not guaranteed ready, and shutdown never drains in-flight sessions.
• You cannot use add_event_handler() to fix this: when the user passed lifespan= to FastAPI(), Starlette stores it as lifespan_context and bypasses on_startup/on_shutdown entirely.

The fix wraps the host app's lifespan_context with an asynccontextmanager that runs the user's lifespan first, then starts the session manager, and on teardown stops the session manager before user shutdown. Wrapping lifespan_context works for both plain apps (_DefaultLifespan still invokes on_startup/on_shutdown) and custom lifespans.

Also adds public startup()/shutdown() methods to FastApiHttpSessionManager and keeps the lazy start as a fallback for apps that never run a lifespan.

Verification

• New tests/test_lifespan.py (6 tests): lifespan events fire with mount_http(), initialize works over ASGI, apps without lifespan still work, and ordering asserts user_startup < mcp_startup and mcp_shutdown < user_shutdown. The ordering test fails on main (session manager never starts during lifespan); all pass with the fix.
• Full unit suite: 75 passed (69 existing + 6 new).

Credit to @Emeralden for the original report and patch in #311.