The `handler` method contained this code in an inline function, which
made the `handler` method big and harder to read. Moreover, this code
relied on variables from the outer scope, which made it harder to reason
about because the inputs and outputs weren't easily visible.
This commit fixes the problems by extracting the file serving code into
a dedicated private method, and modernizing it to use e.g. `const`/`let`
instead of `var` and using template strings.
56d9930a7b