[ElliotEtag]

• Replaces Websim's duplicated deployment steps with the reviewed shared Sites workflow, pinned to 154eec6262d09d1c034c1984caa4503fd3baca75 from feat: share verified Pollinations Sites deployments pollinations#18811.
• Keeps production auto-deploy and the existing production secret; builds without the key, then publishes and verifies on a separate runner.
• Validation: clean install, typecheck, tests, build, actionlint and diff checks pass; all 19 live files match the build. Production verification follows the main → production promotion.
• Reverting this workflow change restores the previous deployment procedure.