Peter's identity is known. Jonah would never hire him, Peter will forever have a role with the Avengers and Stark Industries unless the company goes under or worst gets bought out. There is just no logical reason for Peter to interact with Jonah besides Jonah engaging with Peter to showcase of why he's a menace to society. Jonah character is great because he does have general good points, he's a bit of a hypocrite or is usually plain wrong, but he is a general good guy that creates an obstacle for Peter public reception. Which is why we get the fakeout with Peter "revealing his identity" and then cue him being outed. Tony had the character, intelligence, courage, and wealth to reveal he is Iron Man. Peter is no where near that level, and now he is going to have to face the worst of news media. Which is why having Jonah now is more important then ever for this story angle the writers want to go for.