Has the relation between philosophy and the arts (especially poetry) changed at all since the romantic era?
Of course it has, but not in some clear, fundamental shift. Aesthetics first became a central topic for philosophy with Kant, and shortly thereafter Hegel correctly diagnosed its "death."
By this Hegel did not mean that art would cease to be made and enjoyed. But it could no longer serve as the basis of human development in the Greek or Christian manner, a centrality henceforth to reside in the modern constitutional state, civil society, and the philosophies that rationalize them.
And whither art? While "art" appears more visible than ever, it requires ever more mediation through "theory" or the market to retain a social vitality. It dissolves on the one side into high "concept" and on the other into low, mass "commodity," where it is subjected to critical and sociological theories of commodification, etc.
In general, art became subsumed under "language" in philosophical practices. On the analytical side, art per se no longer held much philosophical interest, with exceptions like Nelson Goodman or Arthur Danto. On the Continental side in the wake of phenomenology, Heidegger essentially dissolved philosophy itself into poetic description. After all, if there is no "real substance" beyond the subject-centered phenomena for philosophy to explicate, then what is philosophy except "redescription"?
There is a great deal of very interesting philosophical work on art, high and low. It continues to be a "topic" for philosophy and critical theory. But the higher hopes for a redeeming aesthetic expressed by Schelling or even the young Hegel in "The Oldest System Programme" appear today the both quaint and tragic.