Improve CI for NAPI-RS (#19983)

This PR updates the CI workflows related to NAPI-RS. So far, we've been
using a custom ghcr.io based image, but these run on Node v18.

With this PR, I created a new project using `napi new`, with GitHub
Actions workflow setup. Then essentially ported the changes from that
new project to this project (as minimal as possible).

The main goal was to be able to bump NAPI-RS related dependencies _and_
get an insiders release out. The images used in these CI jobs were
blockers to get an actual (insiders) release out.

## Test plan

1. CI still passes
2. Added a dry-run on the prepare release workflow to test that we got
through the entire workflow without issues