On what time scale? Julia is really nice lang. but it will take decades for it to put a serious dent in Python. If web side of things matures fast and someone builds a killer framework it might carve out a niche there too.
It's easy to pick up super readable performant lang with good package manager. This already makes it significantly better than a good number of popular web dev. languages.
Julia absolutely is a general purpose language and has been from the beginning. However, there are plenty of languages that are fine for building websites, whereas there are no other languages with the combination of speed and usability that Julia offers in technical computing. It's a lovely language for doing all kinds of work and I personally mostly use it for non-technical computing these days — specifically to implement package management client/server infrastructure, which is mostly web + file system wrangling.
Can you compile Julia programs to native binaries with a singe command ? Can Julia run on mobile and embedded devices ? A real general purpose programming language should do all of those.
True, I'm obviously biased, but at least I can attest to the intention: Julia has always been intended for general purpose computing with the additional (and very challenging requirement) that it be a general purpose language that's also excellent at technical computing, which turns out to be a remarkably hard additional requirement.