Persist room solve history and past sessions

[coder13]

Users want to revisit solves and sessions after the live room is gone.

Feedback source:

• Would it be possible to access past solves, like up to 30 days?
• You could make it so you can look at all your past solves.
• Hello, I would think that scrambles should be seen after having done the solve; they should be kept but disappear when the room is deleted.
• Audio/video feedback also mentioned an option to save the session.

Acceptance ideas:

• Persist completed attempts with enough metadata to review later.
• Decide retention policy, e.g. room lifetime, 30 days, or permanent per-user history.
• Add a UI entry point from profile and/or room session summary.
• Respect privacy/private-room expectations.