Copying into your container is pretty unavoidable, but you’d normally just copy a folder of resources etc. I don’t know the specifics of Elementary but you might be able to do something like Leaf and just copy in a file from a particular directory instead of using a SwiftPM resource
I agree with @0xTim about "just copy the files" - I want to question another thing though: Why would you want to "inline" your style sheet into the HTML?
Since you have a file anyway, just "link" to the file - this usually results in better loading behavior basically for free. Almost by definition style sheets are a lot more "static" than dynamically generated HTML, and boy do browsers like caching things ; )
I would just use some convention about where the assets are going to be and point your file middleware there (either using the bundle stuff or simply some configured folder)