TEIID isn't a supported dialect in jOOQ, and I don't think that the PostgreSQL dialect will get you very far, given how specific a lot of PostgreSQL stuff is. I'd try the H2 or HSQLDB dialects, instead.
In any case, you'll have to do a lot of emulations, like this one, yourself, if you want to run jOOQ on an unsupported dialect. Instead of DEFAULT VALUES, which only very few RDBMS support natively, you can maybe list DEFAULT (using DSL.default_()) expressions for each columns. This is what jOOQ would do for most dialects, anyway. E.g.
insert into form.form_insertdefault_1 (col1, col2, col3)
values (default, default, default);
Or even, just list a single column:
insert into form.form_insertdefault_1 (col1)
values (default);
Or, if DEFAULT is also not supported, pick an arbitrary nullable column that does not have a DEFAULT expression attached to its definition, and insert NULL, there:
insert into form.form_insertdefault_1 (nullable_non_defaulted_column)
values (null);