Can you clarify what your question is here? I'll take a guess, but in case I get it wrong I'd love to confirm.
In any case: I'm the support product lead for DevTools at Atlassian, and as it happens I'm also an ex-support engineer for Bitbucket Server/DC and I'm one of the primary contributors to our official Docker images.
I can confirm for you that we do indeed support our Bitbucket Docker image in production environments. We've put a lot of work into it, so if you have any feedback or run into any issues, please let us know!
Atlassian Team members are employees working across the company in a wide variety of roles.
May 10, 2020 edited
As a general rule we don't recommend one deployment method over another, it all comes down to your requirements. If you're running in AWS, our Quick Start templates are a great place to start. If you're running on your own infrastructure, you might prefer the traditional deployment method of using our installer (or tarball, if you want to customise your service configuration). If you're looking into automating your installation and upgrade process, our Docker images are a great resource to allow you to follow a Configuration As Code model of deployment, i.e. injecting your configuration at runtime rather than modifying configuration files directly.
It all comes down to what you're trying to solve for - however if you are looking at a Docker/containerised deployment then I'd certainly recommend using our official images in production, rather than a third party image or rolling your own
