Fix self-deadlock in handleRoleSelection

[shwetd19]

Fixes #391

handleRoleSelection held room.Mutex (via defer) while calling snapshotRecipients and broadcastParticipants, which both re-lock the same non-reentrant mutex, deadlocking the connection's read loop on every role pick. The lock is now released before broadcasting.

Summary by CodeRabbit

• Bug Fixes
  • Improved room responsiveness during role selection by preventing unnecessary delays in participant and recipient updates.
  • Preserved existing role assignment behavior for players and spectators.

[coderabbitai]

No actionable comments were generated in the recent review. 🎉

ℹ️ Recent review info

⚙️ Run configuration

Configuration used: Organization UI

Review profile: CHILL

Plan: Pro Plus

Run ID: 78cf49f4-50f4-4669-96e6-867ce00dc8a9

📥 Commits

Reviewing files that changed from the base of the PR and between 51532ff and ca5efad.

📒 Files selected for processing (1)

• backend/websocket/websocket.go

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📝 Walkthrough

Walkthrough

handleRoleSelection now explicitly unlocks room.Mutex before spectator returns and before recipient or participant broadcasts. This prevents the broadcast helpers from attempting to reacquire the same mutex.

Changes

Role selection deadlock fix

Layer / File(s)	Summary
Unlock before role broadcasts backend/websocket/websocket.go	handleRoleSelection uses explicit mutex unlocks before returning for spectators and before broadcasting role and participant updates.

Estimated code review effort: 1 (Trivial) | ~5 minutes

Suggested reviewers: priyanshunitr

🚥 Pre-merge checks | ✅ 5

✅ Passed checks (5 passed)

Check name	Status	Explanation
Description Check	✅ Passed	Check skipped - CodeRabbit’s high-level summary is enabled.
Title check	✅ Passed	The title clearly identifies the primary fix: preventing the self-deadlock in handleRoleSelection.
Linked Issues check	✅ Passed	The change releases room.Mutex before helper calls, preventing recursive locking and restoring role selection and message delivery required by issue #391.
Out of Scope Changes check	✅ Passed	The changes are limited to unlocking room.Mutex in handleRoleSelection and are directly related to issue #391.
Docstring Coverage	✅ Passed	No functions found in the changed files to evaluate docstring coverage. Skipping docstring coverage check.

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