Is it possible to manage personal applications on a work profile device?

Yes, as long as the work profile device is company owned. Personally-owned work profile devices offer no personal app management.

For company owned devices, personal usage policies allow organisations to:

1. Set the personal Play Store mode to allowlist, preventing access to the full app store and limiting available applications to only those configured by the administrator.
2. Set the personal Play Store mode to blocklist, allowing full access to Google Play other than applications explicitly blocked by the administrator.

In both cases, applications not permitted to be on the personal profile will be automatically removed.

These policies do not provide any access or visibility to the applications or data within the parent profile. Personal privacy is maintained, but it allows organisations to ensure company owned devices do not run applications unsuitable for an enterprise environment.