I tried adding a public Railway subdomain, but no luck. Getting an error message

Did you map the port correctly?

Make sure the port your site is hosted on is the same port your URL is mapped to.

I did port 80

Let me try 443

No luck with 443 either.

Well this depends on what port Bun is using to host the site.

You have to set the PORT env variable to match

Lemme find docs

Bun isn't hosting the site, I'm building static html files using bun

-# That's if Bun uses PORT no?

https://docs.railway.com/networking/troubleshooting/application-failed-to-respond#application-not-listening-on-the-correct-host-or-port

You'll need some kind of proxy (eg, Nginx) to forward traffic to the site if nothing's hosting your site right now.

How can I configure Caddy or Nginx to do this? I tried using Caddy template, but I couldn't figure out how to feed the build to Caddy

Oh alright in that case you might need to setup a proxy like caddy or nginx to actually serve the content.

Well, one way is to use a Dockerfile.

Alternatively

https://www.npmjs.com/package/serve

You could use a package like this or the bun server to serve your dist folder

That too.
There are lots of ways to host a static site.

Example here:
https://docs.railway.com/deployments/troubleshooting/no-start-command-could-be-found#vite

Good choice!