That in the psalms and they are poetry and song. While poetry speaks of truth we also know it takes poetic license and that not every word is meant to be taken literally.
poetic license
noun
the freedom to depart from the facts of a matter or from the conventional rules of language when speaking or writing in order to create an effect.
No one who take creation literally takes it from psalms.
Psalms can be used as supporting verses but they are not the main verses to be taken literally.
The way the Bible in both the Old and New Testaments speaks of Noah is literal, the same way it speaks of Abraham. No where does it suggest he was a parable.
Noah is included in genealogies and had children.
28 When Lamech had lived 182 years, he had a son. 29 He named him Noah and said, “He will comfort us in the labor and painful toil of our hands caused by the ground the Lord has cursed.” 30 After Noah was born, Lamech lived 595 years and had other sons and daughters. 31 Altogether, Lamech lived a total of 777 years, and then he died.
32 After Noah was 500 years old, he became the father of Shem, Ham and Japheth.
It shows Abraham as a descendant of Noah. The Bible also included Noah in the genealogy of Jesus. Luke 3:23-38
People who were merely Parables characters are not treated like that, only real people were included in genealogies.
Genesis 9:29
Noah lived a total of 950 years, and then he died.
Parables are not given death dates.
Then there are many other verses talking about Noah in both the Old and New Testaments.
Hebrews 11:7
By faith Noah, being warned by God concerning events as yet unseen, in reverent fear constructed an ark for the saving of his household. By this he condemned the world and became an heir of the righteousness that comes by faith.
He is there along with other Old Testament saints.
Directly after Noah it talks about Abraham.
8 By faith Abraham, when called to go to a place he would later receive as his inheritance, obeyed and went, even though he did not know where he was going. 9 By faith he made his home in the promised land like a stranger in a foreign country; he lived in tents, as did Isaac and Jacob, who were heirs with him of the same promise.
After Abraham it mentions Isaac and Jacob. There is no suggestion that the author thought any of the men (and Sarah) mentioned were all parables. Nor would it make sense to insert a parable character in the middle of all the other real people.