I feel like the role of a standard library has become kind of overloaded. Back when you had to manage all your dependencies yourself, having that baseline of functionality bundled with the language and maintained by its authors was a logistical necessity. You just don't have time to chase deps for every little thing.
But in the modern world, I agree with the small language people: the logistical problem is dead. Almost every modern language has push-button dependency management, so the difficulty overhead of using a third-party library is basically zero. And, as you pointed out, this means that the stdlib now competes with third-party libraries, and the third-party libraries proliferate wildly. So there's still a problem, it's just not logistical anymore.
The other problem a stdlib solves is making decisions. This is the npm nightmare: which of these fifty libraries do I use? They're easy to install, but hard to evaluate. This compounds because every library is also making those decisions with their dependencies and so on, so you can end up with 8 different implementations of basically the same thing. You don't have this problem with a stdlib because if there's a std::string, everyone expects your code to work with std::string.
So perhaps the modern stdlib is better off as a standards library: no code, just a mapping from name (ie "option_parser") to package@version (ie "clap@1.1.0"). The work of the stdlib would then be to curate this mapping in a cohesive way, so the packages are high quality individually, but also work well together and reflect the general direction of the language and its community. Whether or not these packages are actually bundled with the compiler is really just an implementation detail. The library isn't code; it's decisions.
Updates would be pinned to release versions, so backwards-incompatible changes coincide with a major version/edition/etc of the language. This would be an expected process, because, as with urllib{n+1}, the first answer isn't always the best. Third-party packages are just as available as ever, of course, and a destandardised package is only a (trivially automated) rename away.
Aside from providing a layer of simplicity and stability over the third-party ecosystem, the standardised libraries would serve as reference implementations for a common interface, like Node's express/connect, or Rust's tokio/futures. In other words, it could help concentrate community effort around emerging standards.
I grant that this is a very, uh, political approach to what has historically been a code problem, but if anything I think the current situation owes itself largely to treating community problems ("how do we agree on a foundational layer of library code?") with technical solutions (package registry + sort by stars).