How can Google WorkPlace Shared Drives be seen by third-party iOS apps?
It sounds like your Workplace administrator has restricted the access to work-related Google services from unmanaged (personal) apps. Which does make sense security-wise.
The solution would be to install your favorite KeePass flavor as a work app. To do so, your Workplace administrator should add the app to the Google Admin console. (Admin Console home → Apps → Web and mobile apps → Add app → … → Make this a managed app.)
Disclaimers: I am the author of KeePassium. The answer is purely theoretical, based on some understanding of app management and Google documentation.