Decide whether lychee should be run on the standalone workflow

[artur-rs]

The problem you're addressing (if any)

The lychee CI check is either skipped or doesn't work. It can be caused by the wrong version of the docker or a network problem. https://results.pre-commit.ci/run/github/202936662/1727443270.BVwXoc4tS5mqTu9cyQeFlQ

Describe the solution you'd like

Let's decide whether to migrate the lychee check on the new CI workflow.

Where is the value to a user, and who might that user be?

Describe alternatives you've considered

Additional context

Relevant documentation you've consulted

Dasharo/docs had the same problem, and it was moved to a different workflow:
https://github.com/Dasharo/docs/blob/master/.github/workflows/seo.yml

Related, non-duplicate issues