Initialize all services with a private DNS name

**Community Note**
* Please vote on this issue by adding a 👍 reaction to the original issue to help the community and maintainers prioritize this request
* Please do not leave "+1" or "me too" comments, they generate extra noise for issue followers and do * not help prioritize the request
If you are interested in working on this issue or have submitted a pull request, please leave a comment

**Tell us about your request**
Currently AppRunner services that are public must communicate over the public internet. If they could communicate over the private network we would gain the benefits of speed and security.

**Describe alternatives you've considered**
Provide a private DNS to all services so they can communicate with each other over a private network instead of the public internet.

No repository files, tests, or implementation entry points are mentioned. Start by investigating how AWS App Runner services currently communicate and how private DNS and private networking are supported; done means all services can communicate through private DNS without using the public internet.

Written by the indexing model from the issue text.