Apple is investing a lot in it, but Swift is much younger than Rust (especially as an open source project). There is a working group that meets every few weeks to shepherd the various projects. Most of the recent activity has been (AFAICT) about orchestration. Well, that and transitioning projects to use async/await and structured concurrency. Here's some recent activity in the Swift on server space:
I'm not pretending that it's taking the server-side world by storm, but there is a fair amount of ongoing activity Personally, I'm using it for a couple personal projects and it's been solid, but I'm already a macOS developer, so it wasn't a big stretch for me to reach for it.
That's just a version number. It's like saying Gmail launched in 2009, because that's when they removed the "beta" label, when people had actually been using it since 2004.
Rust was available in 2012[0], and Swift wasn't until 2014. In reality, since we're talking about using it on the server, Swift wasn't available until almost 2016[1].
They are either the same age or Rust is considerably older, depending on how you look at it:
Rust was publicly announced in 2010, after ~4 years of development in private (starting sometime in 2006, though I don't know how fast that went).[0]
Swift development started that year, 2010, in secret at Apple.[1] It became public in 2014 (some would say it was still in a beta state despite the 1.0 label).