I can't talk about Go much (done very little -- lack of generics is a problem), but I do use C# and I think it's relevant enough.
For context, I have tons of experience with C#, and far less in Rust. With this in mind, C# definitely feels faster to get stuff done initially. This is partly down to more experience with it.
But it's also because the C# standard library includes the kitchen sink, so there's a lot less poking around finding crates and documentation. Async is also much easier. The equivalent of tokio, actix-web, hyper, reqwest, etc are all built in. And you don't do as much thinking up front -- put together some classes and interfaces, throw some exceptions when stuff goes wrong, and you're up and running pretty quickly even with fairly involved async code.
Having said this, I don't think it is actually more productive. There are lots of hidden costs.
When the codebase reaches a certain complexity, I (or we when there are several contributors) forget about all the implicit or explicit design assumptions made, and start discovering runtime errors. Sometimes it's quick to fix; sometimes is takes hours of digging. With Rust, you tend to find more (even most) of these at compile time. Not business logic, but the stupid things: nulls, casts, exeptions, etc. Rust feels slower initially, but it's a lot closer to working correctly the first time.
Refactoring can also be more error prone, especially when you're dealing with a bunch of classes and interfaces because you couldn't just use an neat ADT with pattern matching. Side effects and mutability are another footgun when refactoring.
Another pain point is performance, at least for my use case. A lot of the code I write is very latency sensitive, and a good third of my time is spent on making sure that the code performs well enough. This is actually quite hard in a garbage-collected language. A lot of effort goes into re-designing stuff to reduce heap allocations. And the resultant code, while fast, is a lot harder to maintain -- it's not just plain, idiomatic C# any more: some of it looks more like C. With Rust, it's far less of an issue: idiomatic code is genuinely fast, and without GC surprises.
So while I do think C# is quicker for hacking together a prototype, I'm starting to think that the full lifecycle cost might be tilted in Rust's favour. The hidden costs seem to be less. Provided you don't go down every rabbit hole available 