Infer game code in Web UI

**Is your feature request related to a problem? Please describe.**
After connecting to basalt server through the web UI, the use as to input the game code again.

**Describe the solution you'd like**
Automatically infer the game code when the user connects from the web UI. This should be done in such a way that the user can change the game code if they wish.

Start by tracing the web UI flow that connects to the basalt server and currently asks for the game code. Identify where the connection response and editable game-code input are handled. Done means the code is populated automatically on connection while remaining changeable by the user.

Written by the indexing model from the issue text.