"What method/protocol does foundation use for distributed consistency?"
This is a really tough question to answer succinctly. It took me a long time to wrap my head around it, but the TLDR is:
1. It uses a quorum of Coordinator nodes to elect another node (via Paxos) whose job it is to then assigns roles to other nodes.
2. Some of those roles are replicated (Like TLogs) and some of those roles are singletons (like the thing that advances the clock and hands out versionstamps).
3. If any node in the "transaction subsystem" ever fails, the cluster goes through a recovery where it becomes unavailable for ~3s during which it reassigns the roles and keeps chugging.
In terms of what it looks like for a transaction to actually commit, thats another long conversation. Its hard to draw analogies to existing systems because it really is kind of its own thing.