Overview:
A user is not able to add an existing Object field to a Page Layout for that Object in Vault.
Root Cause:
The object has Object Types enabled, and the Object field has not yet been added to the Object Type that the Page Layout is used for.
Solution:
Add the field to the corresponding Object Type first by navigating to Admin >> Configuration >> Objects >> (Object) >> Object Types.
Related Documentation:
Vault Object Type Documentation: How to Assign Fields