Consider the question regarding "the worldview of extreme materialistic determinism":
What role does desire play in this worldview?
The short answer is that the role desire plays is whatever the narrator of the story of materialistic determinism wants it to play, or, whatever role that narrator can get away with desire playing that will maintain the listeners' interest enough to believe in the narrative, story, or worldview of extreme materialistic determinism.
For example, Chelonian provides one role that desire might play considering the example of a desire to eat "a warm chocolate chip cookie":
Desiring the cookie yet not eating it is consistent with determinism. The deterministic account would say that prior events and the state of your brain caused you to both desire the cookie and abstain from eating it.
This sounds like it might be still a believable role. It might still work, although the very questioning of desire in this context is a challenge. It is like questioning whether Santa Claus can really go down the flue pipe of a modern furnace. And, of course, Santa's narrator can always find an explanation for why that is possible since we humans are very imaginative. Perhaps the empty space in the atoms of Santa and those presents collapse enough, like they do in neutron stars, for him to squeeze by. That might even be labeled a scientific explanation to give it credibility.
Narratives are important. Researchers need to tell a good story to get grant money. They need to convince politicians or institutions to make money available. They need to make sure those with contrary narratives don't have access to that money. Narratives change as social mood changes.
Just because narratives are stories doesn't mean they are false. When Alvin Plantinga called naturalism which is close to an extreme materialistic determinism a "master narrative" (page 311) he wasn't claiming that narratives themselves are bad. Religious beliefs are also master narratives. It just gave him reason to suggest that naturalism is a "quasi-religion".
A change in the materialistic narrative with regards to desire seems to be occurring today with physicians trying to understand what causes auto-immune and other chronic diseases. There seems to be a move away from the genetic cause of the problem to blaming the holobiome, a bunch of organisms living in our digestive tract and on the surface of our skin and surroundings of what we think are our bodies. They send messages to our brains telling us what to desire because that is what they want to eat.
Consider this narrative from Steven Gundry (page 71-2) which could be believable by someone who also believes in the extreme materialistic determinism:
One of our biggest health misconceptions comes from our collective lack of awareness of who we really are. The real you--or the whole you--is actually what you think of as "you," plus those multitudinous microbes. In fact, 90 percent of all the cells that constitute you are nonhuman. To go a step further, 99 percent of all the genes in you are nonhuman.
The narrative appears to be shifting from genes to holobiome. Is that a more interesting and believable narrative? In one very important way, it is. At least we are being reduced to something that could conceivably be viewed as agents with their own desires to eat something sweet like that cookie rather than something oily like a walnut. Conceivably this could introduce free will through these microbes although it is hard to say how we have any of it.
In summary, the question is what role does desire play in an extreme materialistic determinism. Materialistic determinism is a narrative like a philosophical argument, religious explanation or even a piece of fiction. That does not mean it is false. It changes as need be. Desire can be seed as potentially bad microbes causing disease wanting carbohydrates and proteins over better microbes preferring oils. It could also be a prior unconscious brain state if the narrator feels the listeners will find that more believable.
Plantinga, A. (2011). Where the conflict really lies: Science, religion, and naturalism. OUP USA.
Gundry, S. R. (2017). The Plant Paradox: The Hidden Dangers in" healthy" Foods that Cause Disease and Weight Gain. HarperCollins.