Yeah I don't think anyone would really choose to write a new web app with Qt. I assume the target market is people that want to port their existing Qt code to the web. It could also be useful for demoing Qt apps.
Yep, I do it with https://ossia.io (https://ossia.io/score-web) to make the occasional demo ; it's pretty alpha and drag'n'drop still seems to kill it but every Qt release has made it better without me having to do anything.. looking forward to updating!
At one point Nokia pushed the idea that you would write Qt apps to run on their cloud; they had a few actual customers doing it too. I don't know if the current owners kept going with the concept.
It makes sense, from the perspective of shops who invested heavily in upskilling on Qt, to reuse the knowledge to build web apps.
regarding the how.. Qt provides a CMake wrapper which sets up the relevant flags automatically so with CMake/Qt projects it pretty much just works. Here's my build scripts:
I think the better use case for having Qt in the browser is if a web app could benefit from sharing code with a mobile or desktop Qt project. Other than that, yeah, I'm not sure why anyone would use Qt for web apps besides preference.