Node is quite sufficient as web server. It can handle a large amount of requests very efficiently, especially if it is horizontally scalable (which you should do). Go and Rust (don't know about Elixir) would certainly be faster servers, but something makes me think the Node web servers are not the bottleneck.
If the authentication process is the main bottleneck, perhaps you could use JSON Web Tokens (JWTs) to alleviate the load on the database. Using JWTs will allow the client to send back a cryptographically signed token with each request that can be checked at the web server thus decreasing the number of calls to the database.
The Redis-Mongo-MySQL interconnect is a bit weird, though not necessarily wrong. Why all three? What is Mongo's purpose?
There are some other strategies to improve database throughput. There is sharding which helps with horizontal scalability. If your database requests are mostly reads, you can use read replicas on MySQL.