mangum does not cache database connection pools

It appears that mangum runs ASGI lifecycle events (startup, shutdown etc.) on each lambda function invocation instead of run once and cached. This adds an extra ~200ms of runtime to each invocation and can exhaust available database connections unless lambda is calling through a proxy (ex. RDS Proxy) configured to aggressively drop idle connections.

This seems to fix the problem for pgstac:

# app.py

async def connect_to_database(settings: Settings):
    db = DB()
    logger.info("Connecting to database.")
    readpool = await db.create_pool(settings.reader_connection_string, settings)
    writepool = await db.create_pool(settings.writer_connection_string, settings)
    logger.info("Succesfully connected to database.")
    return readpool, writepool

# Define read/write pool in global scope, lambda will cache across invocations.
loop = asyncio.get_event_loop()
READPOOL, WRITEPOOL = loop.run_until_complete(connect_to_database(settings))

# Update startup event.
# Also need to delete the shutdown event.
@app.on_event("startup")
async def startup_event():
    """Connect to database on startup."""
    app.state.readpool = READPOOL
    app.state.writepool = WRITEPOOL

Start from the app.py lifecycle example and trace how FastAPI startup and shutdown events are invoked for each Lambda invocation. Reproduce or inspect the connection-pool behavior across invocations, then verify that pools persist when appropriate and lifecycle setup is not repeated unnecessarily.