The foundation is a set of relatively low tech tools that most people don't know exist, aren't interested in knowing about when you tell them they exist, and can't be bothered to learn how to use even if they were interested.
The World Wide Web isn't one of those foundational tools. It's an easy-to-use added layer that made the Internet marginally palpable to the masses. Nobody wants to go back to the Web as it existed in 1991.
Cookies are another layer that made it possible for websites to recognize you're still the same visitor from one pageview to the next. Without cookies, a Web server forgets everything about you after the page loads. Using cookies automatically gives websites a way to track you, which is the basis of all Facebook fuckery.
JavaScript and AJAX are additional layers that made it possible for websites to further mimic the continuity of desktop programs in a less obtrusive way, with the side effect of providing yet more ways for websites to spy on you without your knowledge or consent.
There's no low-tech way to unfuck the Web now that it's fucked. You can only stay ahead of the fuckery by piling on more technologies: encryption, VPNs, blockchains, private browser sessions, etc. The arms race never ends. That's not getting back to basics.
The free thinkers who remain on the Web will be relegated to backwater sites that can't be found via search engines and other corporate gatekeepers. If you build a website that the corporations don't want to become well-known, you'll be waiting there alone for a mighty long time before someone stumbles upon it.
Returning to foundational principles would basically mean building a transport layer based on a completely different design than the World Wide Web. A number of secure peer-to-peer networks have been designed, but they all depend on a central server knowing about every node on the network in order for one node to find another. That server is a single point of failure that can bring the whole network down or expose all of the peers if compromised.
You would also have to get around ISPs blocking ports that they don't want customers to run a service on. To run a Web server on a residential cable account, for example, you usually have to make the server listen to a non-standard port and use a third-party dynamic DNS service to send visitors to it. Nobody would know to connect to
http://192.168.0.1:8088 unless you publicized it somehow. ISPs are owned by the same assholes that own the media. They make it as hard as possible to do anything other than the usual sheeple stuff.
I'm not saying it can't be done, but it will be a hell of a lot more challenging than opening a Web browser and typing in a URL. People would basically have to create complete online services with specialized client software like AOL and Compuserve on their own dime to approach the level of usability we enjoy on the Web. The owners of those services would more likely than not be petty tyrants with their own TOS and what-not. Being private individuals, they wouldn't be accountable to fairly enforce a clear set of rules. Sites that aren't run by "nazi mods" have always been pretty rare, even in dialup BBS days.
All of that assumes you don't intend to lay millions of miles of new fiber optic cable to create a second Internet that's truly separate from the first, of course. Maybe I'm completely missing what you mean by a second Internet.