Spider-Man's death in Avengers: Infinity War left a mark on Tony Stark, and it may have impacted Tony's relationship with his daughter, Morgan. A lot happened in the five-year time jump between Infinity War and Avengers: Endgame, including most of the Earth's Mightiest Heroes abandoning their posts and going off on their own - even Captain America seemed to hang up his suit and try to move on. But perhaps the most shocking change was Tony Stark living a quiet life.
When the Avengers gather together to ask Tony about the possibility of time travel, he's living in a cabin-like home in the woods with Pepper Potts and their daughter, Morgan. He still has his equipment, but the fact that Endgame emphasizes Tony doing dishes shows how grounded he's become, no longer the playboy (or narcissist) the Iron Man trilogy made him out to be. Logically, having Morgan must've changed Tony's perspective on life and his choices in being a full-fledged superhero. But there's a sense that Spider-Man's death forced change upon Tony as well.
It wasn't Iron Man's fault that Spider-Man died on Titan, but Tony still carried that guilt with him for five years. He recruited Peter Parker to fight with him in Captain America: Civil War and then he later tried to induct Spider-Man into the Avengers in Spider-Man: Homecoming. Tony pushed Peter to become a better hero, and in turn, Peter pushed Tony to become a better father-figure, which ultimately made him a better father. Peter wasn't just Tony's "trial run", but rather someone he felt that he let down, so he did everything in his power to make sure it didn't happen again - especially to his daughter, Morgan.
Despite the Avengers having a plan to bring back everyone who was killed by Thanos' snap, Tony first refused to help; he told Scott Lang that he couldn't risk his life with his daughter on a gambit like time travel. At that point, he finally understood the true consequences of his actions as Iron Man. Sure, he tried to have the Avengers sign and abide by the Sokovia Accords, but that was in regards to accountability; this was about personal sacrifice. But Pepper knew better; she knew Tony wouldn't be able to "rest" if he didn't try to rescue everyone.
The Iron Man trilogy taught Tony Stark to care about the world and forgo the profits from his company's weapons program; the Avengers movies, as well as Captain America: Civil War, made Tony realize the consequences of being a superhero; and Spider-Man's death humbled (and scared) him on a fundamental level, which in turn grounded him. Everything that made Tony the iconic Tony Stark/Iron Man withered away with Spider-Man, and instead he became a better person and a better father to Morgan.