'Rediscovery' I think clearly applies to: from Romanticism - which was far more dominant and lasting in philosophy in Germany than in England. John Vervaeke has a great lecture on Romanticism in the context of the history of philosophy, which was all news to me. I can't think of a figure like Goethe in the English speaking world, able to contribute significantly in natural philosophy, and make a lasting impact with poetry also. Maybe Thoreau.. It's notable Thoreau followed the post-Socratic traditions of cynics and Stoics, focusing his philosophy on ordinary life, and with a kind of existential introspection. Also, that he was a very marginal figure in his lifetime who's significance was only recognised later (unlike Goethe!).
The Analytic Philosophy tradition diverged from the arts, to adhere more to the models of mathematics & logic as templates, and consideration of what art is and is for, has ceased to be a central point of discussion. Whereas the Continental Philosophy tradition has been greatly affected by literary analysis and consideration of a far wider range of types texts as having philosophical import, or have cultural significance that has philosophical import, allowing literature & poetry being contemplated to be considered 'serious philosophy', rather then kept in a seperate cultural domain. Nietzsche and Kierkegaard, primary influences on Heidegger, saw art as a central concern.
There is an example of the contradictions that come from the limiting of philosophy to certain types of language, that came up in discussing the category of water: Is steam necessarily ice? There is a tendency to, rather arbitrarily distinguish between 'factual' and 'poetic' use of language, and regard the latter as frivolous and essentially, meangless - as the OP did there. But as Wittgenstein observed, language is use: "How did we learn the meaning of this word? From what sort of examples?"
Poetry is part of our use of language. We use metaphor so much we don't even notice: joining the fray is a metaphor from weaving we apply to battle, when moving we weave from side to side, and shuttle is another weaving term applied to spaceships! Much of this extending of language has come from poetry; the kennings of Darraðarljóð in the Njals saga made me notice the prevelance of weaving metaphors; chortle and gallumph have entered the language from The Jabberwock, a poem set expressly at creating portmanteaus, another word from the Alice books; 1498 words or phrases were first attested in Shakespeare. I would look to WW1 poetry, and the early writing of Bob Dylan like Pawn In Their Game (sung at the same podium Martin Luther King Jr later that day gave his I Have A Dream speech from), for the cultural significance with philosophical import, of poetry. They said things in ways facts couldn't, that helped contribute to changing how we live.
Heidegger's ontology of time, is an essentially experiential and personal view, the idea of 'throwness' into circumstances, and that the full context of our lives can be only be understood from the perspective that they are finite. This is a kind of somatic, experiential, and poetic experience, of time, and knowledge of death. He viewed our own being as shaped by our doing, including rituals, architecture, and cultural practices - he saw the lived practice of these as actually shaping and changing the reality we live in. Our widest frame is what makes a life worthwhile, and of course if poetry is an important part of that for people, that makes it a philosophical concern, and/or the consequences of ceasing to value poetry in this way.
An example I think Heidegger would approve of, a poem commonly recited at funerals, that has so entered our language that it is part of the language of how we die, of how we approach death, and the reciting of which helps people live out a shift of attitude tomone that is more philosophical:
"Death, be not proud, though some have called thee
Mighty and dreadful, for thou art not so;
One short sleep past, we wake eternally
And death shall be no more; Death, thou shalt die." - John Donne
So if we address what it means to die, and how we die, that would fail I think without considering poetry. The Illiad is a much older example of holding a cultural record of war and death and grief, Hecuba being a kind of archetype of those raised up and thrown down by fate (mentioned in one of 13th C Carmina Burana poem like that). Ecclesiastes is considered a profoundly subversive book of the Old Testament, at odds on many points with the other parts, but I would say the participatory, recitable nature of it explains why it is there, and why it is read both at weddings & funerals, and even became a pop song:
"To every thing there is a season, and a time to every purpose under
heaven: A time to be born, and a time to die; a time to plant, and
a time to pluck up that which is planted; A time to kill, and a time
to heal; a time to break down, and a time to build up; A time to weep,
and a time to laugh; a time to mourn, and a time to dance" - Ecclesiastes
'This too shall pass' and 'Know thyself' are strictly more aphorisms than poetry, but have gone on to influence literally millenia of philosoohy and literature.
Philosophy that ignores the significance of these kinds of experience, is impoverished by that. Philosophy that ignores the nature and purpose of art, has chosen early defeat in pursuit of understanding truth, wherever it leads. It is a modern folly to divide these out of the concerns of philosophy
(although I admit, Plato wanted no poets in his Republic; his involvement in the politics of Syracuse was, startlingly inneffective however, and I'm with Popper's judgement of him).