Is it possible to view smart group membership in Views?
You can join to any CiviCRM table with the Views CiviCRM Expose Tables module, so you can join to civicrm_group_contact_cache.
I'm not savvy enough about smart groups to know when this is reliable - this table gets destroyed and regenerated on a regular basis, and may come up empty sometimes.  However, since this is for internal use, you could have some way to guarantee that the cache is full (e.g. by regenerating it as part of the user's workflow).
Another option to consider is Search Kit, if you can upgrade to newer versions of CiviCRM.  It's very Views-like, and can give you a configurable set of columns.