Enhancement: POTD countdown doesn't swap the problem at IST rollover (needs a reload)

[barunaniket]

What happened?

NextProblemCountdown counts down to IST midnight, but when it reaches 00:00:00 it silently restarts near 24h without swapping in the new Problem of the Day. A page left open across the rollover keeps showing yesterday's problem until the user reloads. (Fresh loads are correct — the solve pages are force-dynamic.)

Steps to reproduce

1. Open /cp-arena (or a solve page) shortly before IST midnight and leave it open.
2. After the countdown hits zero, the timer resets but the problem shown does not change.

Affected page / URL

/cp-arena, /cp-arena/solve/<slug>.

Where did you see this?

Both.

Suggested fix

At rollover, refresh the daily problem (re-fetch / soft-navigate) or show a clear "A new problem is live — refresh" prompt instead of silently restarting the timer.