Properly use context managers for async SQLAlchemy connections

[holtgrewe]

Is your feature request related to a problem? Please describe.
We do not properly use context managers for the async SQLAlchemy connections. We then get errors The garbage collector is trying to clean up non-checked-in connection <AdaptedConnection <asyncpg....

Describe the solution you'd like
Review all code such that we properly use context managers everywhere.

Describe alternatives you've considered
N/A

Additional context
N/A

[holtgrewe]

I only found one place in deps.py but I'm uncertain whether this can cause issues.

Also, looking into whether we can use lifespan to force shutting down the engine.