This is not so much something that went wrong but a way to make the App work a little better on Mac. For Proton VPN when you hit CMD W, or click the red circle, it removes the icon from the Dock but it is still working in the background.
For most Mac Apps, including Proton Mail, hitting CMD W, or clicking the red circle, closes the visible App but leaves the icon in the dock. This lets you quickly open the App again.

It would be nice if Proton VPN acted the same way.