An end-user is adding a budget to a newly created Event. The end-user is a Team Member but does not seem to have visibility to the budget record.
The budget object is set as Organization-Wide Defaults (OWD) Private intentionally. Being an Event Team Member does not allow access to a budget record, but does allow access to an Event Budget record.
With Event Management, it is recommended that the owner field on a budget record is set as the end-user. The reason for this is due to the role hierarchy. When an end-user is the owner of a budget, users above this user in the hierarchy are able to see the budget record. Conversely, this prevents users equal to or below this user on the hierarchy from viewing the record.
Another alternative is to ensure budget records are appropriately shared with end-users.
The role hierarchy enables users above another user in the hierarchy to have the same level of access to records owned by or shared with users below. Consequently, users above a record owner in the role hierarchy are also implicitly granted Full Access to the record, though this behavior can be disabled for specific custom objects. The role hierarchy is not maintained with sharing records. Instead, role hierarchy access is derived at runtime.