"Play Again" sends participants to the landing page

[TheCodeHeist-Coder]

On the final screen, participants get a button labelled "Play Again".

apps/frontend/src/screens/LiveQuiz.tsx:684:

<Link to={isOrganizer ? "/dashboard" : "/"} ...>
  {isOrganizer ? "Back to Dashboard" : "Play Again"}
</Link>

It navigates to / — the marketing landing page. The participant has to find the
join entry point again and re-enter a code and nickname from scratch.

"Play Again" promises to start another game. Landing on a homepage with hero
copy is not that.

Fix. At minimum, point it at /join.

Better: JoinQuiz already reads location.state?.code and
location.state?.username for its initial values, so the nickname can be
carried over:

<Link to="/join" state={{ username }}>

That is a one-line change using a mechanism already built into the screen — the
participant then only needs the new code.

Consider the label too. If the same quiz is over, "Play Again" is slightly
misleading regardless of destination; "Join another quiz" describes what actually
happens. Your call — mention which you chose in the PR.

Definition of done:

• The button goes somewhere a participant can immediately join from
• The nickname is prefilled if it can be carried over
• The label matches what the button does