Is Railway suitable for hosting software development environments?

Not sure exactly what you mean by this alone, can you give some examples?

Where is the source code located for the templates?

Templates are not represented as code, they are made and configured through the template composer web UI that can be found here - Template Create

Is there specific information you are looking for?

Sure. Suppose I chose the template: "Vite + React - The default Vite + React starter, with Caddy"
That appears to be a developer setup (for software development), but is it actually just hosting a project that I've already created? I don't want to spend all my trial allowance to find out. :-)

That template deploys an example React app that uses Vite for tooling, and Caddy to serve the website.

The template itself is not codified, but it does deploy the React app from a GitHub repo, for any template that deploys from a repo you can open the template page, scroll down and click on the link to the repo - https://railway.app/template/NeiLty

After you deploy such a template from there you can eject from the template and Railway will clone its original repo into your github account and you can work on the repo and make changes to it.

In the template composer, after I select a Github repo, how does it know what my infrastructure requirements are?

I think you may be confused, you probably want to make a project, not a template.

Go back to your dashboard and create a new project.

I'm trying to deploy locally:

$ railway link 55a1afbe-XXXX-XXXX-be78-ce0ae43712eb

error: unexpected argument '55a1afbe-XXXX-XXXX-be78-ce0ae43712eb' found

Usage: railway link [OPTIONS]

For more information, try '--help'.

$

Why is it failing?

railway link is typically used as an interactive command, run it without any arguments.