perf: optimize React component rendering with memoization

[Copilot]

React components were recalculating expensive operations on every render. The Wheel component filtered participants and computed SVG paths each render, while RoomLayout performed redundant array lookups.

Changes

Wheel component:

• Memoized eligibleParticipants filtering (eliminates O(n) operation per render)
• Memoized SVG sector rendering (caches trigonometric calculations)

// Before: recalculated every render
const eligibleParticipants = safeParticipants.filter(
  p => p.status === ParticipantStatusEnum.QUEUED || p.status === ParticipantStatusEnum.ACTIVE
)

// After: cached until participants change
const eligibleParticipants = useMemo(() => {
  const safeParticipants = Array.isArray(participants) ? participants : []
  return safeParticipants.filter(
    p => p.status === ParticipantStatusEnum.QUEUED || p.status === ParticipantStatusEnum.ACTIVE
  )
}, [participants])

RoomLayout component:

• Memoized currentPresenter lookup (avoids array iteration per render)
• Memoized lastWinner calculation (prevents object recreation)

Analysis

Not optimized:

• Room entity defensive copies: Required for DDD immutability guarantees
• Configuration service JSON operations: Only called at startup/dev hot-reload
• Timer panel intervals: Already follows React best practices

Full analysis documented in docs/PERFORMANCE_ANALYSIS.md.

Original prompt

Identify and suggest improvements to slow or inefficient code

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