Currently I am learning Dapr, and I find it powerful for micro services development, but after reading more, I found some limitations, the most important of them is "state management".
How can we use tools like EF Core or Dapper for interaction with databases in Dapr? Is DaprClient class the only way of interaction with databases?
You should continue to use those ORMs alongside Dapr as its not a replacement for them. ORMs already act like a translation layer (Repository layer) for relational stored data. State management is simple KVP storage with some minimal query ability. Think of your state as a Dictionary<string,object>, where that object can be anything simple or complex. this is well suited for technologies like Redis, DynamoDB, MongoDB, Cassandra etc. Again, what you would put in cache, is what you would put in state storage. So, you can still (and should) have an ORM in your service for relational data and pass in runtime configuration for provider, connection string etc, while being able to utilize all the other features of Dapr via DaprClient, via HTTPClient or via GRPC clients.
Bonus, with many providers in EFCore/EF you can add tracing headers (https://github.com/opentracing-contrib/csharp-netcore) that will seamlessly plug into the tracing provided for free with Dapr. That way you will see a full e2e trace all the way through your state and relational data