feat(ci): update build tooling

[WikiRik]

Updates the rollup version we use and introduces a separate build step in the CI so we test on the files that will also be published to npm. This also allows us to more easily update eslint in a future PR. It's a feat because there might be (very) minor changes to the build itself.

This incorporates part of the changes of #2401

Checklist

• [X] PR contains only changes related; no stray files, etc.
• [ ] README updated (where applicable)
• [ ] Tests written (where applicable)
• [ ] References provided in PR (where applicable)