Rename the root package to `ai_gateway`

What does this merge request do and why?

Step 1: This MR renames the root codesuggestions package to ai_gateway.
Step 2: Rename the suggestions package - TBD with a follow-up MR.

Please, note that this MR affects the Dockerfile, several Makefile targets, and pyproject.toml.

How to set up and validate locally

To validate that everything was renamed correctly, you can follow the next steps:

• run tests
• build a Docker image
• run affected Makefile targets
• run the server locally or in the stg cluster

Merge request checklist

• Tests added for new functionality. If not, please raise an issue to follow up.
• Documentation added/updated, if needed.

Ref #290 (closed)