Build and Test both the Dev and Production Webpack Asset Process

[feanil]

Context

The static assets check workflow only builds the dev version of the webpack assets and as such does not test that the production webpack config will build properly. This is partly due to the fact that the assets paver commands make it difficult to test the production webpack build without configuring a more production like edx-platform python settings.

Furthermore, the paver commands are deprecated and alternatives already exist which make it easier to build either the dev or production webpack assets.

Acceptance Criteria

• Update the statics assets check workflow to use the new non paver commands to compile assets.
• Update the workflow to build both the dev and production assets.

[kdmccormick]

Thanks for the reminder. Now that the DEPR is accepted, it's good time to switch the CI check from Paver to the new thing.

Ready for review, assuming tests pass: #34836