If I create a new schema on the current database (management), why does it complain about cross-database references?
management=# create schema mgschema;
CREATE SCHEMA
management=# alter table clients add column task_id int null references mgschema.tasks.id;
ERROR: cross-database references are not implemented: "mgschema.tasks.id"
alter table clients add column task_id int null references mgschema.tasks.id;
The REFERENCES syntax in not correct, you should use:
REFERENCES reftable [ ( refcolumn ) ]
A simple references only expects a table name. The foreign key will then automatically point to the primary key of that table, e.g.
alter table clients add column task_id int null references mgschema.tasks;
Another alternative is to to specify the table and columns, but not with a single identifier:
alter table clients add column task_id int null references mgschema.tasks (id);
The second format is needed if the target table has multiple unique constraints.