At the end of the day, it's not that people forgot Peter. It's that he gave up everything he held dear. It was the emotional equivalent of Tony's snap.
He sacrificed it to save everyone. To make sure his kids have a future. He died a hero.
Peter loved his family. And friends, but his identity was a problem. So he gave up his "life," in his own way, to save them.
That's why I think, when peter said 'We won, Mr Stark." And "I am sorry, Tony." Hurts so much. Because Tony Stark always found a way to live through all the disasters in his life. For Peter, he was a hero first. Every title came after. His belief that Parker Luck won't hurt him like it did to Uncle Ben. But that was shattered.
And it was his first lesson winning always doesn't mean you won. Hence, it was easier for him to do what his dad did. Because this was the world, his dad died to protect.
Peter understood that. Because Iron Man did something Tony Stark wouldn't do. Who wants to leave their kids and die to save the world, but he did. That's why Spider-man has to do things that hurt Peter Parker.
The whole Tony Stark - Not recommended, and Iron Man - Recommended debate doesn't have to be disrespectful.
It's more like Tony is human, but Iron Man is a hero. Like when he flew the nuke to wormhole or save people during the expo. Peter is a human who could use his powers for anything, but he chose to be a Spider-man, a hero.
Their are so many parallels like obie and Beck. Both were people they trusted. For peter, he didn't believe in spidy sense because of the grief and pain of losing his Hero, Mentor, and Father-figure again. Just like Tony trusted obie after losing his parents and Jarvis. And get betrayed, then continued to fix their mess.
And in a sense, you can see Tony's influence on Peter as well. It's kind of melancholic, how we can see bits and pieces of Tony in him.
You can't always hold your parents. You forget their voices, their laugh, their smell, and so many little things, but you will always carry bits and pieces of them for those who remembered to see. Just like happy saw Tony in Peter.