How can I include pug templates in compiled typescript

Question

My nodejs based application uses Pug for rendering; specifically, i set the view engine and then set the view directory (which lives inside of the src directory that all other source lives in.

app.set('view engine', 'pug');
app.set('views', __dirname + '/views');
[...]
res.render('login')

This works correctly for the development version, which simply runs and interprets the typescript file that the above code is in. However, I would like to compile to javascript in production, and have the following (seemingly standard) typescript configuration:

{
    "compilerOptions": {
        "target": "esnext",
        "module": "CommonJS",
        "esModuleInterop": true,
        "skipLibCheck": true,
        "forceConsistentCasingInFileNames": true,
        "outDir":"./dist",
        "rootDir": "./src"
    },
    "$schema": "https://json.schemastore.org/tsconfig",
    "display": "Recommended",
    "files": ["src/index.ts"],
}

Which reflects the directory structure of my code:

Unfortunately, this fails to work when the application is compiled and ruins index.js; it cannot find the .pug files in /dist/views: Error: Failed to lookup view "posts" in views directory "/app/dist/views"

I understand the error message, but not how to fix the problem. Should I be copying the templates to that folder as part of the build process? Should I be invoking them in another way that the compiler can 'understand' and include? Is compiling typescript to javascript simply an obsolete build step entirely?