enhancement: Cache active map lookup in RingCollisionSystem — O(n) per tick is too slow

Description

`RingCollisionSystem.findActiveMap()` iterates over all entities every tick to find the entity holding `ActiveMapComponent`. With 8 players, this is 8 linear scans per tick (160/s). As entity count grows this becomes a performance bottleneck that will manifest in tick overruns.

Acceptance Criteria

• The active map is cached in a field on `RingCollisionSystem` (or via a dedicated `ActiveMapCache` helper)
• Cache is invalidated/updated on map transitions (when `ActiveMapComponent` changes)
• `findActiveMap()` is no longer called inside the per-player tick loop
• Micro-benchmark or comment documents the before/after complexity

Technical Details

• Simplest fix: store the game entity reference at system initialization time; access its `ActiveMapComponent` directly
• Or: introduce an `EntityManager.getSingleton(Class)` convenience method for single-entity components
• Applies the same pattern fix to any other system doing per-tick entity scans for singleton components

Dependencies

• Phase wiring must be complete (so the game entity exists when the system initializes)

Estimate

S

Start at RingCollisionSystem.findActiveMap() and trace how ActiveMapComponent changes during map transitions and how phase wiring creates the game entity. Check whether caching the entity reference or adding EntityManager.getSingleton(Class) fits the existing lifecycle, then verify that the per-player tick loop no longer scans entities and document or benchmark the complexity change.