BenchmarksGame is actually an interesting if unfortunate case for C#.
Many tests there are at odds with the areas of optimizations that get most engineering effort investment in .NET: high level and/or application logic and high-performance primitives like Span, Vector, etc. (with the exception of perhaps Regex-Redux, but even there I'm not sure why the results are so low, because C# has one of the fastest[0] regex engines that only loses to Intel Hyperscan, Rust one and PCRE2).
Probably the best way to go about this is to just give it a try with a sample project and see if the RAM usage is to your liking - you can get far with plain 'dotnet new console --aot' and standard library (once you're done, .NET's variant of go/cargo build is 'dotnet publish -o {output folder}').
Overall, .NET tends to have higher memory footprint than Go because its GC is designed to sustain much higher allocation rate and heaps spiking to much higher use without severely throttling performance (which Go does). But there are interesting developments with the new GC mode called DATAS. I made a very simple example project some time ago to showcase .NET's concurrency and publishing experience to someone else which shows that it now rivals Go where it's the strongest[1].
[0] https://github.com/BurntSushi/rebar#summary-of-search-time-b...
[1] https://github.com/neon-sunset/http-bench