[Feature] Implement backend integration for joining game sessions

[milospi]

Description

Implement the ability for a user to join an existing session using a valid game pin.
Requirements covered:

FR5: User can join a session using a valid game pin
FR6: System validates the game pin before allowing access

Acceptance criteria:

Player enters a game pin and clicks "Join"
Invalid pins show an error message
Valid pins add the player to the session in Firestore and navigate to the lobby

Related requirement

No response

Architecture layer

None