I showed my mom how she can use 'web.whatsapp.com' to use Whatsapp more easily (in order to share screenshots or links with others).
After logging in, a notification about Whatsapp having been installed from the app store popped up after a few seconds. And indeed, the Desktop app had been installed, without any user interaction whatsoever.
I am not even sure how this was initiated, but I believe DoH being disabled by default probably has to do with it.
Edit: Like a lot of comments have suggested, I most likely remember this wrong. I tried to reproduce this (after "forgetting about" whatsapp.com in Firefox and uninstalling the app) and was unable to. I did encounter three separate "install the app" buttons, all of which however yielded an additional installation prompt from the app store.
Apologies.
FWIW, according to https://developer.mozilla.org/en-US/docs/Web/Progressive_web... Firefox does not support PWAs without an extension, so that wasn't it either.