There's no need for a new internet. Every garbage service has a somewhat viable alternative.

You have peertube instead of youtube Kagi, duckduckgo, marginalia, etc instead of Google search Lemmy instead of reddit Mastodon, polycentric instead of twitter Gitea instead of github Bandcamp instead of spotify There are probably more things but you get the idea. The problem is not the internet itself but that you have to have many people go to objectively less polished or paid services to protect their personal data. I don't know how that would happen since honestly, the privacy shit doesn't affect people's everyday lives, but using different services does affect their lives.