feat(bot): clock-aware time management and stream-driven tournament play

Tournament bots flagged in 5+3 classical: budgets were fixed and
clock-blind, HybridBot's veto re-search double-spent (up to 4s/move),
and the game loop polled every 1s, burning our clock waiting on the
opponent.

- Bot is now a trait taking a TimeControl (remaining + increment);
  apply(ctx) defaults to Unlimited so local/self-play/tests keep their
  fixed budgets.
- TimeControl.budget derives a per-move budget from the real clock with
  an overhead reserve, a panic mode under 20s, and a hard ceiling, so a
  bot can no longer flag from thinking.
- HybridBot splits one budget across main (0.7) and veto (0.3) searches
  instead of running two full searches.
- TournamentBotGamePlayer reads the server clock (seconds -> ms) and
  plays stream-driven via GET /game/{id}/stream (NDJSON, heartbeat-kept),
  so the opponent's move arrives instantly; polling stays as a fallback.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

modules/official-bots/src/main/scala/de/nowchess/bot/Bot.scala

@@ -3,4 +3,33 @@ package de.nowchess.bot
 import de.nowchess.api.game.GameContext
 import de.nowchess.api.move.Move
 
-type Bot = GameContext => Option[Move]
+/** Remaining wall-clock for the side to move and the Fischer increment, both in milliseconds. [[TimeControl.Unlimited]]
+  * is the sentinel for callers without a real clock (local play, self-play, tests): bots then fall back to their own
+  * fixed budgets.
+  */
+final case class TimeControl(remainingMs: Long, incrementMs: Long):
+  def isClocked: Boolean = remainingMs >= 0L
+  def budgetMs: Long     = TimeControl.budget(remainingMs, incrementMs)
+
+object TimeControl:
+  val Unlimited: TimeControl = TimeControl(-1L, 0L)
+
+  private val OverheadMs = 1500L
+  private val PanicMs    = 20000L
+  private val MaxBudget  = 8000L
+  private val PanicCap   = 2500L
+  private val FloorMs    = 50L
+
+  def budget(remainingMs: Long, incrementMs: Long): Long =
+    val usable = math.max(0L, remainingMs - OverheadMs)
+    if usable <= 0L then FloorMs
+    else if remainingMs < PanicMs then clamp(usable / 15 + incrementMs / 2, PanicCap)
+    else clamp(usable / 30 + incrementMs * 4 / 5, MaxBudget)
+
+  private def clamp(value: Long, ceiling: Long): Long =
+    math.max(FloorMs, math.min(value, ceiling))
+
+trait Bot:
+  def move(context: GameContext, time: TimeControl): Option[Move]
+  def apply(context: GameContext): Option[Move]                    = move(context, TimeControl.Unlimited)
+  def apply(context: GameContext, time: TimeControl): Option[Move] = move(context, time)