Session handling for authentication and user preferences will not work as expected in Cloud Run or Any scalable environments.
Because most of the application works with a memory-based implementation to perform this function. However, this implementation is unsuitable for an app that can be served from multiple instances, because the session that is recorded in one instance might differ from other instances.
So you must store it in a commonplace where all the instances refer to the session info.
For Cloud Run available solution as of March 2020,
you can spin up Redis on Compute Engine(Costly! of course)
You can use a Redis instance from Redis Labs
You can use Cloud Firestore. (cheap, but not an efficient solution)
Note: Cloud Firestore is a persistent, distributed, transactional database. Often, it's more appropriate to choose a different storage solution for sessions such as Memcache or Redis as their designs offer much faster operation in this use case.
Here is a doc with an example for Nodejs: https://cloud.google.com/nodejs/getting-started/session-handling-with-firestore
For other known Cloud Run Limitation so far. check here