Improve integration test suite CI run script

Created by: eseliger

The final result in the CI logs

Otherwise this PR does the following improvements:

• Fixes the CSS modules types generator when run outside of the repo root (client/web, for example)
• Fixes a deprecation in the Webpack dev server, which I saw along the way
• Adds the CSS generator to the set of generators run for build-web. They were missing there
• Share the set of generators to run for build-web, so this issue doesn't arise again
• Switch to a different run script where yarn generate isn't run twice
• The above grouping of log outputs into "steps"