Use game repository with all game-related requests

[the-only-queen-anna]

As a developer, I want to have more uniformity in the way the frontend code cooperates.

Currently, the game view model has knowledge about the web socket handler, which is not ideal and should be changed.
Therefore, we want to redirect all calls that are currently directly aimed at the web socket handler over the game repository to ensure better capsulation and better testability, like we already have with the Lobby and Chat Repository.