I finally tested on a fresh install... and it works. So I dug some more, comparing the two installations, and realized at some point is a JS error on my regular install, linked to the chat integration plugin. In the end the code was outdated (it relied on a deprecated API), so I pulled the last version from git and... it worked.
Long story short: this was a plugin bug 🤷 Sorry for the noise, and thanks for suggesting testing a separate install!
@bmann I guess https://github.com/discourse/mail-receiver is the repo? Did I understand correctly that it can be run on a separate server and hooked up to Cloudron+Discourse install? (Of course, ideally, we can have this all part of the Cloudron package itself or maybe a separate Cloudron package)