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 In the end the code was outdated (it relied on a deprecated API), so I pulled the last version from git and...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!
Great - adding the subdomain in Cloudron and setting up Amazon SES login for that fixed the issue so I can now both send (via SES) and receive emails (via a Zoho pop mail box), including reply by email mode.
Thanks for your advice everyone!
I tried this now in a fresh install and it seems to work.
Please note that you are supposed to run the commands in the app's web terminal (i.e Click the gear button in the cloudron dashboard app -> Console -> Terminal). And then you must put in sudo -E -u cloudron bundle exec script/rails console in the shell. Like below: