Difference between the comic angle and movie are in the comics, Peter didn’t quit for anywhere near the time that he did in the movie and there were at least others who could pick up the slack. In this case, he willingly quit knowing full well that he was the only thing that stood between New York and disaster, worse yet by just how much things had escalated compared to his first outing.
Also at what point did the concept of being someone’s protege suddenly become sidekick because honestly I don’t think anyone who calls him such knows what it means no offense. Robin to Batman is a sidekick. They do what they do as a duo. Peter was green in this version and Tony brought Peter into the bigger game of superheroics but left him to do his own thing beyond that aside from when Peter royally screwed up, just as any mentor would do. Any point that Peter ended up with Tony such as Infinity War was Peter choosing to in spite of Tony trying to keep him safe (which also speaks a lot of Peter’s character as a hero). Hell Peter had to handle things entirely on his own with no assistance from Tony when it came to dealing with Vulture and then later Mysterio. And before anyone says that he used Starktech to create his new suit, yes, he used the tech but the suit’s creation was all him down to every spec of what went into the suit. That moment represented the full on point at which Peter steps out of of Tony’s shadow by not using either suit he made for Peter but the one he made himself, the culmination of the story arc Far From Home was going. The entire prospect was getting to see the character grow and develop over time rather than just rushing at it and suddenly they’re a pro overnight.