As some of the previous commenters said, when you focus your language to make it easy to write a specific type of program, then you make tradeoffs that can trap you in those constraints like having a runtime, a garbage collector and a set of APIs that are ingrained in the stdlib.
Rust isn't like that. As a system programmer I want none of them. Rust is a systems programming language. I wouldn't use Rust if it had a bloated stdlib. I am very happy about its stdlib. Being able to swap out the regex, datetime, arg parsing and encoding are a feature. I can choose memory-heavy or cpu-heavy implementations. I can optimize for code size or performance or sometimes neither/both.
If the trade-offs were made to appease the easy (web/app) development, it wouldn't be a systems programming language for me where I can use the same async concepts on a Linux system and an embedded MCU. Rust's design enables that, no other language's design (even C++) does.
If a web developer wants to use a systems programming language, that's their trade-off for a harder to program language. The similar type safety to Rust's is provided with Kotlin or Swift.
Dependency bloat is indeed a problem. Easy inclusion of dependencies is also a contributing factor. This problem can be solved by making dependencies and features granular. If the libraries don't provide the granularity you want, you need to change libraries/audit source/contribute. No free meals.
A feature present on every language that has those in the stdlib.
The de facto standard regex library (which is excellent!) brings in nearly 2 MB of additional content for correct unicode operations and other purposes. The same author also makes regex-lite, though, which did everything we need, with the same interface, in a much smaller package. It made it trivial to toss the functionality we needed behind a trait and choose a regex library appropriately in different portions of our stack.
Regex is not 3rd party (note the 'rust-lang' in the URL):
All those AFAIR need 3rd party packages:
Regex, DateTime, base64, argument parsing, url parsing, hashing, random number generation, UUIDs, JSON
I'm not saying it's mandatory, but I would expect all those to be in the standard library before there is any http functionality.