It's worse than you thought.
The webmail provider released a dedicated browser that can only open the webmail and called it a "desktop" app.
Additionally, they don't support IMAP. There's an app to run on your computer that becomes a bridge. The proprietary protocol is translated to IMAP. You can't use your favorite client if your operating system can't run that bridge and you're not a premium user because for "reasons" only premium users can run that local bridge