missing-root I remember them using the Signal protocol, and storing messages forever on a blockchain.
The only time I read up on Session the situation was as it is now. The network needs some nodes to route messages with some degree of anonymity, and also to hopefully-briefly store messages while endpoints are hopefully-briefly offline. This has some structural similarities to the needs of the Tor network, though the hopefully-brief storage part is different.
The Tor network historically relies on volunteers to run the nodes. My understanding of Session is that they are trying a different idea, namely to piggyback message transfer on nodes that are participating in a blockchain network. The fact that the same computers are doing both jobs does not imply that Session messages are stored on the Oxen blockchain, or ever were stored on the Oxen blockchain.
Whether the idea of piggybacking non-blockchain functions on blockchain nodes will work out is unproven. But at least in theory it would be possible to migrate Session to a volunteer store-and-forward network similar to Tor's volunteer forwarding network.