When I use surrealist things, I try to keep them confined to some particular area or concept or the like. Over-use quickly leads to boredom: "oh, another kuh-ray-zee thing, yawn, moving along..." (Not that my players have ever said this to me; it's just been my experience in other contexts and from others' reports.)
So, for example, I have emphasized the "outsider-ness" of certain beings by using certain phrases with my players. "You open your magical senses and you can see...well, it's really hard to describe. The couatl you see was also the human-looking woman from earlier...but now, with your magical senses open looking at her natural form...you can see that she's somehow more than she should be. That it's almost like she's...folded up, being squeezed into a space smaller than she actually is."
Other beings, those who are merely touched by this outsider-ness without actually being outsiders themselves, have similar descriptions but to a lesser degree. So, while Tlacalicue (lit. "Daylight-Her-Skirt") is a proper celestial, Tenryu Shen the gold dragon is only partially outsider-like, and thus has "less" of the too-much-person-squeezed-into-space effect. Recently, I had another character (a time dragon "stuck" on the barrier blocking exit from the world the PCs come from) who was similar, but his existence was divided between different locations (one "inside" the barrier, one "outside." He got stuck because someone did something very stupid with an artifact that has space-time properties.)
In other areas, I do things like mentioning unusual sensory combinations, playing up the spooky vibes, providing background music when I can (RIP Rhythm Bot, it sucks people kept using you illegitimately...) and otherwise enhancing the overall "feel" in various ways. Doing too much more just risks being overblown or failing to deliver.
I lean into surrealism when angels or other extra-planar creatures are interact with the party. Sometimes slightly off occurances happen when the party is travelling through a plane fairly distant from the Mortal planes.
surrealism is a way to go outside official path and expectation.
For DnD the Fey wild may be the most ideal place to play surrealism, making a toad the absolute ruler of the Fey kingdom and reversing usual expectation for monster, classes and so on.
For fantasy my best take is the « Save the cheerleader, save the world » from the heroes tv show.