Basically, they clearly don't police individual users self-hosting, but they maintain the right to knock on the door of companies.
Redistribution is also not allowed.
The Bitwarden desktop and mobile clients are open source because they are under GPLv3, a license that meets the OSD. Vaultwarden is also GPLv3.
(By the way, the only widely accepted definition of open source software is the one published by the OSI, and the only widely accepted definition of free/libre software is the one published by the FSF, so those are the definitions we use.)
The license for this code https://github.com/bitwarden/server/blob/master/LICENSE_BITW... says,
> 2.4 Third Party Software. The Commercial Modules may contain or be provided with third party open source libraries, components, utilities and other open source software (collectively, "Open Source Software").
which implies that the Commercial Modules, themselves, are not Open Source Software.
(Also it clearly doesn't follow the Open Source Definition or any other standard definition of Open Source.)