docs: Add AsyncSession and async tools tutorial (#626)

[alexbthundiyil-spec]

Fixes #626. Adds comprehensive tutorial documentation for using SQLModel with async engines and FastAPI async dependencies.

[mahdirajaee]

The tutorial is a useful addition, but there are a few technical issues worth addressing. First, the variable name sqlite_url is misleading when it holds a PostgreSQL connection string ("postgresql+asyncpg://..."). This will confuse readers following along — should be renamed to something like database_url or async_url. Second, the create_heroes function calls session.commit() and session.refresh() but has no error handling — an async tutorial should ideally demonstrate try/except with rollback, or at minimum mention that exceptions during commit leave the session in a broken state and need await session.rollback().

Third, the FastAPI integration example references engine and Hero without imports or definitions, which means it won't run as-is. Since this is a tutorial, each code block should either be self-contained or clearly reference the earlier block. Finally, the get_session dependency yields a session but doesn't show what happens on exception — FastAPI's dependency injection will call session.close() via the generator cleanup, but session.rollback() on error is a common pattern that's worth showing for write operations. The read-only example is fine as a starting point, but a note about write endpoints needing explicit rollback handling would round this out.

[alexbthundiyil-spec]

Thanks for the feedback! I've addressed all the points:

1. Renamed sqlite_url to async_url since it's a Postgres connection.
2. Added try/except with await session.rollback() to the create_heroes function.
3. Updated the FastAPI integration block to be fully self-contained (added the imports, the model definition, and engine initialization).
4. Added a POST endpoint to the FastAPI example to explicitly demonstrate the session.rollback() pattern during write operations.

Let me know if there's anything else you'd like me to tweak!