"RAFT uses a protocol that looks awfully like Paxos for election of a single leader"

Agreed.

"so it has nothing to do with multi-Paxos (as I understand it)"

Except that Raft is not only a protocol for single leader election, it's also a replication protocol (see the "AppendEntries" message), and that's why it is Multi-Paxos. Multi-Paxos is just the category or classification for a family of consensus protocols that use the strategy of single leader election and replication with terms/views/epochs (the "interim regime" you refer to) for strict serializability. This is the passive replication leader/follower primary/backup strategy.

Outside of Multi-Paxos, there are also consensus protocols that achieve strict serializability with Paxos but without electing a single stable leader, e.g. FastPaxos. These exploit low latency between the client and all replicas, but this is not always available, or may suffer from tail latency issues, hence implementations such as Raft use the MultiPaxos strategy of a stable leader, which may be better connected to the rest of the cluster than the client.

As an implementation, depending on how you zoom, Raft is very different to VR and ZAB, but it's still in the same Multi-Paxos class since it reuses a single stable leader derived from one instance of Paxos for "multiple" rounds or instances of replication, hence "Multi-" "Paxos".

At least this is how I understand it from Heidi Howard and others who seem to share this "view".