fix: persist participant session secret after password verification

[BackGwa]

Description

This bug fix ensures that participants in a private room can correctly decrypt and read the host’s chat messages after password verification.
Previously, the participant-side session secret was not persisted after verification, which caused encrypted chat payloads to be uninterpretable.
By saving the verified participant password into the session secret state, the participant flow now keeps the required encryption context for chat decryption.

Type of Change

• Bug fix (bugs/)
• New feature (features/)
• Refactoring (refactor/)
• Hotfix (hotfix/)
• Chore (chore/)

Related Issues

Peers cannot interpret the host’s chat in a private room. #30

Changes Made

• Persisted the participant session secret immediately after successful password verification.
• Added setSessionSecret(participantPassword.trim() || null) in the private-room connection flow.
• Ensured participant chat encryption/decryption context is available when moving forward to ParticipantPage.

Checklist

• Code follows the project's coding style
• Self-review completed