Why are Vault Owners unable to change a Study's State field?
This is caused by the following setting: Admin --> Settings --> Application Settings --> Enable Lifecycle for Study, Study Country and Site. Enabling this setting creates Object Lifecycles for the Study, Study country, and Site Objects. The Study State field is then controlled by the record's Object Lifecycle and is no longer editable from the in-line viewer.
Note: once this setting is enabled, it cannot be disabled.
This is expected behavior. The system manages the Status field based on which Lifecycle state the Study is in. Users can leverage User Actions to move Study's from one State to another.
Vault eTMF Documentation: Lifecycles for TMF Objects