Do not start the container manually during tests action

[sambarza]

Description

We start the container just to run the tests however the launched instance is not used by the tests, FastAPI's TestClient doesn't need the Cat to be running; it starts the Cat instance on its own for each individual test.
Removed the up and down steps.

This should also speed up the tests step too.

Using docker exec instead of docker run because exec needs an already running container, while run creates the container before starting the command. docker run need the service name instead of the container name.

Not related to issue.

Type of change

• Bug fix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Breaking change (fix or feature that would cause existing functionality to not work as expected)
• This change requires a documentation update

Checklist:

• My code follows the style guidelines of this project
• [X ] I have performed a self-review of my own code
• I have commented my code, particularly in hard-to-understand areas

[pieroit]

Awesome, also for climate change :D