It is not possible to update or create choice records in a specific application scope. Even when creating choices(sys_choice records) for a field in specific application scope, the sys_choice record becomes read-only in that application scope and on switching to Global scope to edit the record, the Table field becomes empty and users are unable to edit the choice record correctly.
You may also see an error message like
Invalid 'Table' selected on the Choice record.
The '[TABLE_NAME]' table is in application '[APPLICATION_NAME] but the current application is 'Global'.
This issue is seen because even though the sys_choice records don't have any application scope, these choice records belong to a 'sys_choice_set' which has an application scope defined.
If the application scope of this sys_choice_set is created in global, but the choice records are being created for a table which is in a specific scope, the choice records behave as though they are in the global scope and therefore this issue is observed.
To confirm if this is what is causing the issue for you, navigate to the sys_choice_set table and filter the list by the table and the element (field for which the choice records were created) where the issue is experienced. Note that the Package and Application fields for the sys_choice_set are set to Global although the table belongs to a different scope. This mismatch confirms the root cause.
The application scope for the 'sys_choice_set' records cannot be changed once the record is created. The only way to resolve this issue would be by deleting the faulty 'sys_choice_set' record which exists in the global scope but the table that it belongs to lives in a different application scope. This step to delete the sys_choice_set can only be done from the global scope.
Once the deletion is completed, make sure to switch your scope to the specific application scope and then create new sys_choice_set records for the corresponding table and the elements.
Please note that this would also remove the existing choices that you have for these fields and these will need to be created again. We would recommend keeping a record of the choice records so that you can create them again.