It’s worth testing at least, to see if there are any gaps in the new package’s capabilities. It’s a lot less mature, and not as modular if you only need client code and not server functionality. Having the HTTP parser components be in pure Julia instead of C will be useful, if it turns out to be comparably robust and reliable.
I’d say look over the code, compare it to what’s in the existing web stack and judge for yourself whether the old code or the new would be easier to understand and fix if it came to that. Currently if something breaks in HTTPServer.jl and you’re not using that piece, then it doesn’t matter much for you. Whereas with all of the code in a single package, some types of problems even in code you’re not using could get in your way.