How come you compile your app on your deployment platform? I know Heroku does this, but wouldn't it be easier to compile your Rust app on a beefy CI server and then just ship a binary or container image to your deployment infra where you can size the server according to runtime load.
E.g. I use Fly.io for one of my apps. I build a container image as part of CI on Github Actions and then just push that image to Fly as part of a deploy. Fly never deals with a build step (although it can do that as well).
$5 is very cheap for the Hetzner server you describe though.