While i am not aware of a browser that behaves like you described exactly, i vaguely recall that there is a browser plugin that is similar to what you described

While i am not aware of a browser that behaves like you described exactly, i vaguely recall that there is a browser plugin that is similar to what you described....but can't find it right now. That being said, there is a search engine named Wiby [https://wiby.me https://wiby.me] that focuses "...building a web of pages as it was in the earlier days of the internet.", so maybe that be nice to check out?