[FR]: Simple example of using `run_binary()` with `out_dirs`

### What is the current behavior?

I'm trying to figure out if `run_binary` is appropriate for my use case, but I can't determine where my `tool` should write its outputs for them to appear. However, there's no simple examples of this attribute being used I can easily understand, and I can't use makevars or location to find my `out_dirs`.

### Describe the feature

rules_pkg has a directory of [examples](https://github.com/bazelbuild/rules_pkg/tree/main/examples) that make it relatively easy to figure out how to use the rules from looking at some simple to moderately complex examples. I'd love to see something similar for `run_binary()` since its only "genrule" that has the `out_dirs` capability.

Related info:
* I did try looking at this [issue](https://github.com/aspect-build/bazel-lib/issues/228) but I couldn't quite wrap my head around it
* I also tried looking at the source code for [rules_js](https://github.com/aspect-build/rules_js/blob/d55c9de0da18bf303060c35ef43b78ada88dcd75/npm/private/npm_import.bzl#L700) but I couldn't easily jump through the project to figure out how all of that works

Start by reviewing the repository's examples directory and the run_binary documentation or implementation, alongside the linked rules_pkg examples. Add a simple, understandable example that demonstrates where a tool writes outputs when out_dirs is used; done when the example is discoverable and explains the expected outputs.

Written by the indexing model from the issue text.