The code, when running, can readily distinguish between them (e.g. for development vs. production) environments, say to run different libraries between each.

I use environment variables for that. You don't want the code to do autodetection based on the environment, because you benefit from having development/staging/production servers to be very similar.

A single body of code can be deployed, without change, and it will run appropriately in each case.

There are pre-made solutions for that, see Plack.

The code that does it is simple, reliable, self-evident

When dealing with different webserver environments? Surely you must be joking.

The best you can do is reuse well-test solutions. They can be reliable, and maybe their usage is simple, and evident from the documentation.