Or you can use read only Redis replication and keep your architecture pretty much the same https://redis.io/topics/replication
What happens when that replication breaks? Can people still log in? Can you still validate their sessions? Or are you going to have an outage in a geographical region?
Fall back to connecting to the main instance directly
And if the replication is down because the main instance can't be reached for a minute?
If all the servers are in one location, a random byte sequence as session id key with cached info is the most simple, compact and efficient.