Account switching does support both SaaS cloud users, and self-hosted instances to be connected and switched between with the desktop app with the new feature. Please see
If you appear to be having issues connecting your self-hosted account to utilize this account switching feature then the self-hosted instance may not be running the official installation and instead be running the 3rd party unofficial fork known as Vaultwarden.
This has been a known issue and tends to give an error “Logged out Your login session has expired.”