Dreams Come True (2018) by Parky.
From RoyalRoad:
In a futuristic world of superheroes and supervillains, the ability to dream of another world doesn’t seem that applicable nor useful. But for Demund, who has recently sent off his best friend to the superhero training grounds—the Preliminary Islands— it was nothing but life-changing. For him, a rejuvenating vacation to a world of magic is now only a good night’s rest away.
As Demund explores his new world, reality around him begins to change. How will he manage to balance their existences together?
Demund and his friend are ranked D+ and B+, respectively (chapter 1.1):
“B+? not bad. You’ll definitely pass the Selection with that score.”
“It’ll satisfy my parents well enough. So, what did you get?”
Jothan carefully put his evaluation sheet back into his packet. Demund’s packet was on his desk, still unopened with the glue intact on the lid. Demund stared at it. He predicted that he would not make the Selection, but still had a faint hope from what the examiners had told him. Maybe…just maybe his score was high enough. He might be able to join his friend on the Islands after all. Or his wishes were unanswered and he’d stay in his everyday, bland life just like the majority of the population.
“You really want to see? It’s probably much lower than yours.”
“But I want to know whether you’ll go to the Selection with me or not.”
[...] Demund reached his fingers inside, pinched the paper, and lifted it up for Jothan and himself to see. To their surprise, they found a rather disappointing score.
“A D+.”
Demund loses a leg to a car accident (chapter 4.3):
“What’s wrong with your leg?” asked a student while Demund was packing his things. His arms were crossed, and he had a frown on his face—his lips were pursed. “Got into an accident?”
Demund looked up from his bag and stared directly into the student’s eyes.
“It got run over by a car. They had to amputate it,” he said with a smile.
Found with the Google query scifi other world dreams site:royalroad.com.
