#280 print start/finish timestamps for job progress

[VasilevNStas]

baza.rb polls finished? without any indication of whether the job actually started or how long it's been running. The user sees only "waiting..." until the polling timeout.

What this PR does

Adds ISO 8601 timestamps around judges update:

Job 79196 started at 2026-06-29T20:15:30Z
... (judges output) ...
Job 79196 finished at 2026-06-29T20:16:45Z

What this enables

Scenario	Before	After
Job starts	No signal	"started at ..." visible in stdout
Job completes	Only judges output	"started at ..." + "finished at ..."
Job crashes	Nothing, baza.rb hangs	"started at ..." only — signals abnormal exit

If judges update fails (non-zero exit), set -e means only the start timestamp is printed — which itself signals that the job started but didn't complete normally.

Checklist

• bundle exec rubocop — 0 offences
• bundle exec rake — all tasks pass
• HoC ≤ 133

@yegor256 please review

[VasilevNStas]

Why this matters

baza.rb polls finished? with a timeout. When the timeout expires, it has no way to tell whether:

• the job never started (config error)
• the job is still running (slow judges)
• the job crashed silently (no stdout at all)

After this PR, every job produces:

Job 79196 started at 2026-06-29T20:15:30Z
... judges output ...
Job 79196 finished at 2026-06-29T20:16:45Z

The key insight: if you see started but no finished, you know the job crashed. If you see neither, you know it never started. This turns a blind timeout into actionable diagnostics with zero added complexity.