Peter could also be a bit conflicted. He might not want to be treated differently just because he's Tony's son. He wants to be recognized for his own achievements as Spider - Man. So, he could try to prove himself even more to the Avengers, showing them that he's his own hero, while still being proud of his connection to Tony.
Peter might be really nervous at first. He's used to being just the friendly neighborhood Spider - Man, and now the Avengers know he's Tony's son. He could be worried about living up to their expectations.
Peter is likely to be in awe. He might be a bit nervous at first, but also extremely excited. He has looked up to the Avengers for a long time, so meeting them would be like a dream come true. He would probably be stuttering a bit as he tries to introduce himself and show his respect.
They might be a bit surprised at first. Maybe Tony makes some jokes about British tea and bad teeth, but in a friendly way. Steve would probably be intrigued by Peter's different cultural background and might ask him about British history.
Some Avengers might be initially shocked. For example, Steve could be a bit taken aback as he tries to understand how this could be possible. He might be concerned about the implications for the team dynamics.
They could react with surprise. After all, Peter is still young. But then they would likely be happy for him. Maybe they'd offer to take MJ out for a nice dinner to get to know her better.
They might be shocked at some of the dangerous situations Peter has been in without their knowledge. They could feel guilty for not being there to protect him more. And they would likely be very proud of his selfless acts.
The Avengers would initially be in shock when they find out Peter is sick. Clint Barton would be the one to keep a calm head and start organizing things. Wanda Maximoff would try to use her powers to ease Peter's pain if possible. Vision would use his vast knowledge to try and find a solution. They would all be very concerned and do everything they can to make Peter better, from getting the best medical help to providing a safe and comfortable environment for him to recover.
The Avengers might react in different ways. Steve Rogers would probably be polite but firm in getting to know Peter's boyfriend. He'd want to ensure that he was a good influence on Peter. Thor, on the other hand, might be a bit more boisterous. He could either be really friendly and enthusiastic, or his loud and powerful presence might accidentally scare the boyfriend a bit.
One way is by getting involved in Peter's school life in a more official capacity. Maybe they could arrange for some anti - bullying seminars at the school. Natasha could also train Peter in stealth and evasion techniques so that he can avoid the bullies more easily. Thor could even offer to be Peter's bodyguard for a while, at least until the bullying situation is resolved.
Peter would probably have a closer relationship with the Avengers, especially those who were close to Tony. For example, he might have a special bond with Pepper, who would be like a mother figure to him. And he would be seen as more of an insider from the start compared to his normal origin. He could also get more direct training from the likes of Captain America or Thor.
Peter would likely have a closer relationship with the Avengers. He'd be like a little brother to some of them. For example, Thor might take him under his wing and teach him about Asgardian lore. And Captain America would be a great role model for Peter in terms of leadership and moral values.