We need to build wheels in the public CI because

• it generates a log that can be audited by both team members and external stakeholders when an issue happens (ex: cuda-python 11.8.5/12.6.2 package content issues #226)
• the artifacts can be inspected and reused (ex: moving to internal artifactory for QA/release processes)
• wheel contents can be tested as part of CI
• it is automated instead of relying on anyone on the team to manually navigate, which can be error-prone and cause delays

TODO:

• Check in the internal build tool
• Set up a build CI (Set up a public, GitHub-Action-based CI infrastructure #81)