I'm unfamiliar with Rust, so I'm mostly going to address the little I know about Go. It's a great language if you want low memory consumption, concurrency and a fairly simple codebase - the language is minimalistic and C-like so it tries to shove complexity away. I'm someone who hasn't touched anything with pointers in ages and really loved it. Docker, Kubernetes, Terraform and from what I've heard a lot of Google services are being developed in Go, think about what they have in common and if you have a similar use case or you specialize in backend and devops then GO for it.
However people are reporting that Rust is coming to the Linux kernel soon so it seems like a solid choice no matter what you pick.
I think I have a similar background to you and learning Go definitely made me a better programmer and it barely took any time.
(Self promotion ahead, skip to last paragraph) I even made an article[1] that's an introduction to Go where I talk about everything that seemed interesting to me and I follow up with a small project, it's meant for junior to mid level developers that want to start with Go or are undecided. Perhaps have a quick look (it's been well received and featured in Hashnode).
Overall I'd highly recommend learning Go, it was a breath of fresh air for me after working mostly with Node and Spring Boot. If I had to make a backend system, depending on the requirements, Go would definitely be a top choice for me.
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[1]https://bognov.tech/introduction-to-golang-build-a-mini-twit...