To whom it may concern,

Although in documentation is not specified, you if emulator is running in docker you need to set

- AZURE_COSMOS_EMULATOR_IP_ADDRESS_OVERRIDE=127.0.0.1

Answer was actually here: https://stackoverflow.com/a/75757385

If somone needs, this is basic docker-compose.yaml file that works.

services:
  cosmosdb-emulator:
    image: mcr.microsoft.com/cosmosdb/linux/azure-cosmos-emulator:latest
    container_name: cosmos-db-emulator
    ports:
      - "8081:8081"
      - "10250-10255:10250-10255"
    environment:
      - AZURE_COSMOS_EMULATOR_IP_ADDRESS_OVERRIDE=127.0.0.1
      - AZURE_COSMOS_EMULATOR_PARTITION_COUNT=3
      - AZURE_COSMOS_EMULATOR_ENABLE_DATA_PERSISTENCE=true      
    restart: unless-stopped

Just to point few more things.

• Number of partition is reduced to 3, which means it will create 4 partitions :) (look at the running emulator log).

• Also emulator is quite slow to startup, so be patient.

• If you don't want to import certificate then you can do this:

  CosmosClientOptions options = new()
  {
    HttpClientFactory = () => new HttpClient(new HttpClientHandler()
    {           ServerCertificateCustomValidationCallback = HttpClientHandler.DangerousAcceptAnyServerCertificateValidator
    }),
    ConnectionMode = ConnectionMode.Gateway,
  };
  
  
  using CosmosClient client = new(
      accountEndpoint: "https://localhost:8081/",authKeyOrResourceToken: "C2y6yDjf5/R+ob0N8A7Cgv30VRDJIWEHLM+4QDU5DE2nQ9nDuVTqobD4b8mGGyPMbIZnqyMsEcaGQy67XIw/Jw=="
     , clientOptions: options
  );
  

• Otherwise import certificate: https://learn.microsoft.com/en-us/azure/cosmos-db/how-to-develop-emulator?tabs=docker-linux%2Ccsharp&pivots=api-nosql