Context

Follow-up to #4727 / PR #4739 (HA auto-acquire of never-seen databases). Code review noted that
ArcadeStateMachine now carries a fair amount of database reconcile orchestration on top of its
core Ratis StateMachine contract. This is a non-blocking code-health item, deferred out of #4739 to
avoid late churn on a converged PR.

Scope

Extract the reconcile orchestration into a dedicated DatabaseReconciler collaborator, leaving
ArcadeStateMachine focused on the Ratis state-machine contract. Candidates to move:

• reconcileDatabasesFromLeader(...) and refreshExistingDatabases(...)
• the pure helpers classifyReconcile(...), executeReconcilePlan(...), applyReconcileOutcome(...),
  bumpFailureAndShouldRetry(...)
• the per-database state: acquireStatuses and acquireFailureCounts (+ the AcquireStatus /
  AcquireState / ReconcilePlan / ReconcileOutcome types and the getAcquireStatus /
  getDatabasesWithAcquireState accessors used by GetClusterHandler / ClusterAlerts)
• the give-up constant ACQUIRE_GIVE_UP_AFTER

Considerations

• notifyInstallSnapshotFromLeader and notifyLeaderChanged would delegate to the collaborator
  (the leader-change cleanup of LEADER_MISSING / FAILED statuses + failure counters).
• The unit tests in ReconcilePlanTest reference ArcadeStateMachine.classifyReconcile /
  executeReconcilePlan / applyReconcileOutcome directly; they would move to target the new class.
• GetClusterHandler and ClusterAlerts call getAcquireStatus / getDatabasesWithAcquireState,
  so the accessors must remain reachable (likely via the reconciler instance held by the state machine).

Pure refactor - no behavior change.