If every energetic action in the universe is expressed as a wave function, then why would it be mystical for the fabric of spacetime to function in a (probability) wavelike manner? Why would a curved spacetime be mystical?
The question what is mystical and what not is, obviously, not a very well-defined one. One can start here with
https://en.wikipedia.org/wiki/Mysticism (using Wiki as the collection of mainstream prejudices, which is quite sufficient here). It points to some psychological part connected with personal experiences, which is irrelevant here, it is the other part which is relevant here, described by phrases like "understanding of ultimate truths" "In mystic states we both become one with the Absolute" or "supplies knowledge of the transcendental". "an extreme and intense form of the insight seeking process that goes in activities such as solving theoretical problems"
"direct consciousness of the [...] the ground of being".
A particular variant of mysticism which is closely related with science is the mystification of mathematical structures, with numerology as the most well-known example. There is even a particular entry
https://en.wikipedia.org/wiki/Numerology#Numerology_in_science about its role in science in Wiki for this. The often mentioned "beauty" of the mathematics of particular theories (with GR as a leading example) is, essentially, also a harmless description of some aspects of this mathematical mysticism. In this connection, I highly recommend to download somewhere the book Fuchs, Fomenko, Gutenmacher, Homotopic topology to look at the pictures.
So, what is the role of mysticism in science? First of all, the motivation of the mystic - to understand the Absolute, the Ultimate Truth - is clearly also part of the motivation of a scientist. Then, if one observes strange mathematical coincidences, this may be a starting point for a scientific discovery. Some mystical "eightfold way" may become a theory of quarks and chromodynamics.
https://en.wikipedia.org/wiki/Eightfold_Way_(physics) One may think that this buddhist naming was a joke, but it was a quite subtle one, and one should be at least aware of this part of buddhism to make such a joke. Another famous example is Kepler, who was motivated by astrological thinking. So, roughly speaking, mystical thinking is a natural element of scientific thinking during the search for new theories.
But this is the "free flight of imagination" part of science, the part which is not restricted by any scientific methodology, a necessary intermediate step for the creation of new scientific theories. This part should be finished somewhere, giving a theory which is not obliged to give spiritual insights into the Ultimate Truth, but real predictions about things we can measure with ordinary human measurement devices.
And this is the place where the GR spacetime interpretation has gone wild. The four-dimensional curved spacetime is a nice and fascinating metaphysical, mystical speculation, which may play an important role for mystical speculation, which can, possibly, allow some scientists to invent some theory of quantum gravity or of everything. But this is only a speculative, mystical Ultimate Truth. What we have in reality, supported by observation, is something much more prosaic. It is a quite boring theory about the distortions of our clocks and rulers by gravitational fiels and their own velocity relative to these gravitational fields. And from the point of view of search for Ultimate Truth this theory is even frustrating, because it tells us that these distortions prevent us from measuring Absolute Time and Absolute Space.