I admit that I last worked with it in early 2020, but at the time there were numerous annoying open bugs with the Swift compiler on Linux (such as the installer messing with the Python path), and then there was the issue of divergence between Foundation (which is closed-source) and its Linux replacement. Meanwhile, the stack size for secondary threads was ridiculously low and there was no good story for fault recovery (because you don't want to crash your server if you accidentally access an invalid array index).
Maybe things have improved, but I'm doubtful.
On the Linux front, there's Apple's SwiftNIO which is a generic lower-level framework that itself is not an out-of-the-box web or API framework. You need another extra layer above it, which is for example this community-driven project called Vapor [2]
You can, in principle, build a e.g. JSON API based on barebones SwiftNIO and you will save a lot of 3rd party dependencies in this case, but this path is a bit masochistic, you really need to know what you are doing in this case. Vapor is much easier to jumpstart any kind of server project with.
Sorry but this can't be more wrong. I love Swift so much that I can tolerate and forgive its compiler's sluggishness.
Swift is now available on Linux (has been for a while) and there's Apple's server framework called SwiftNIO. It's designed for fast and efficient multithreaded server-side code. I voluntarily picked it for my next backend project and am very happy so far.