Channel access at scale

Design the permission layer for a team chat product where access to a channel depends on workspace membership, channel membership, and per-channel role, and the UI must render 'which of these 2,000 channels can I see?' on app load in under 200ms. Membership changes constantly (people added/removed from channels), and a removed user must immediately lose the ability to read new messages. Walk through how you store and evaluate channel access, how you serve the bulk 'list my visible channels' query fast, and the invalidation problem when membership changes.