Make timed mode a real session: gate the start, run one countdown, show results on expiry

[RagibAhashan]

Problem

Timed mode today is per-challenge and the clock is loose:

• The countdown doesn't start until the user types — they get unlimited thinking time before the timer engages.
• The countdown is per-challenge: every advance restarts the clock, so there's no notion of a session score or pace.
• When the timer expires there's no payoff — it just advances to the next challenge silently. There's no place to see how you did.
• Average time per challenge is recorded as ~0 ms for motion-only challenges, because the elapsed timer is started inside the same call that detects success.

Proposed behaviour

Make timed mode a fixed session you race against:

• Blur the editor with a "Press space to start" overlay until the user explicitly begins. This applies the first time timed mode is engaged in a session — subsequent challenges flow without the gate.
• Once started, run a single countdown for the whole session. It does not reset between challenges. Solve as many as you can before it hits zero.
• When the countdown expires, replace the editor with a results view: accuracy, avg time, avg score, fastest, and a per-challenge time chart. Include a restart button that reshuffles and re-arms the gate.
• Start the elapsed timer the moment a challenge becomes interactive (not on first state change), so motion-only challenges record real time.

Out of scope

• Untimed mode behaviour stays the same.
• No persistence of session results across reloads.