Automate dead link checking

### Problem to solve

### Proposal

From Comment in #281:

> This tool could be helpful to automate the dead link checking and help solve this issue:
> https://github.com/lycheeverse/lychee
>
> One idea is to build a local production version of the project, open it in preview and then run lychee against the local site. This tool can output in multiple formats, which might even be used to automatically flag and potentially filter out projects with the broken links.

### Links / references / screenshots

#281

Start by reviewing issue #281 and the linked lychee tool proposal, then locate how the project is built and previewed locally. Define the automation around the production preview and decide what link-check results should report or filter; done means the dead-link check runs consistently and exposes broken links.

Written by the indexing model from the issue text.