After some investigation, I don't believe the issue is related to the attribute method. The entire received reply is empty. There are no headers or body received by the application. The Wireshark capture shows that the entire message is properly sent out by my HTTP server and received by the browser, however, the application does not receive it.
I checked if any error was reported by the reply and received an error QNetworkReply::ProtocolFailure (399). I believe the browser strips that information and does not propagate it further to the application. I tested this in Firefox and Chrome with the same results.
As I mentioned in my original post, the communication works perfectly when compiled as a desktop application. The issue was only observed when compiled by WebAssembly.
I will close this post and reopen a new one with a new question.