Whether Spider-Man has done, or will do, something to earn his new place among the heroes is not clear.
It’s done in a very “matter of fact” sort of way that clearly indicates that making Spider-Man an Avenger isn’t the most important thing going on right now.
If you were expecting a lot of pomp and circumstance, possibly a ceremony of some kind, then you’re probably disappointed.
It feels like Tony might be doing the kid a favor by making him an Avenger as a token, considering they may all be dead by the time this is all over.