You will need to install the Postman Desktop Agent if you are using the web client and you want to access local resources. The requests are generally sent from the Postman cloud which will not have access to your local resources (10.x.x.x are local addresses).
Therefore the DNSLookup error is correct in that instance. The web client will not be able to resolve that local IP address without the postman agent.
The ETIMEDOUT error is different and could be caused by various issues. It means that its connected to the IP address, but is not getting a response in a timely manner. The first step is usually to check your local firewall settings even if you are running the desktop client on the same machine as your docker container. Whenever Postman gets updated, I normally get a windows prompt to allow access through the local firewall. Did you see such a prompt? You also need to check that your application is running. Perhaps by running an independent check with cURL to check connectivity.
I did see the windows prompt today, when opening the Postman app on my laptop, and checked the box to allow private networks to access the application.
I finally got the request to work and return an expected response, I had to tweak a connection string setting in a database table that the microservice, that handles authentication, calls to get a security token.
Request Headers