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Use the inject_variables method.
It has an optional parameter verbose, which defaults to True.
Set it to False if you want less noise.
Example.
Slightly simplified version of the code in the question:
sage: L = LieAlgebra(QQ, 3, step=3)
sage: L
Free Nilpotent Lie algebra on 14 generators
(X_1, X_2, X_3, X_12, X_13, X_23, X_112, X_113,
X_122, X_123, X_132, X_133, X_223, X_233)
over Rational Field
sage: A = GradedCommutativeAlgebra(QQ, names=L.basis())
sage: A
Graded Commutative Algebra with generators
('X_1', 'X_2', 'X_3', 'X_12', 'X_13', 'X_23', 'X_112', 'X_113',
'X_122', 'X_123', 'X_132', 'X_133', 'X_223', 'X_233')
in degrees (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)
over Rational Field
Let us inject variables:
sage: A.inject_variables()
Defining X_1, X_2, X_3, X_12, X_13, X_23, X_112,
X_113, X_122, X_123, X_132, X_133, X_223, X_233
Or with less noise:
sage: A.inject_variables(verbose=False)
The generators are now available and have the correct parent and type:
sage: X_1
X_1
sage: parent(X_1)
Graded Commutative Algebra with generators
('X_1', 'X_2', 'X_3', 'X_12', 'X_13', 'X_23', 'X_112', 'X_113',
'X_122', 'X_123', 'X_132', 'X_133', 'X_223', 'X_233')
in degrees (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)
over Rational Field
sage: type(X_1)
<class 'sage.algebras.commutative_dga.GCAlgebra_with_category.element_class'>
