Add colored circle badge showing affinity client count before the account
status indicator. Badge color reflects count severity (gray=0, green=1-5,
yellow=6-15, red=16+). Tooltip shows full client ID list on hover.
Backend: AccountHandler batch queries reverse affinity index via
GetAccountAffinityClientsBatch, returns affinity_client_count and
affinity_clients in DTO. GatewayCache interface extended with the new
batch method backed by a Lua script (get_affinity_clients.lua).
All test mocks synchronized with updated GatewayCache interface.
Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>