build: build docs in GitHub Actions CI workflow

Backport-PR-URL: https://github.com/nodejs/node/pull/32608
PR-URL: https://github.com/nodejs/node/pull/31504


Reviewed-By: Jiawen Geng <technicalcute@gmail.com>
Reviewed-By: Luigi Pinca <luigipinca@gmail.com>
Reviewed-By: Rich Trott <rtrott@gmail.com>