What I did:
Switched work computers which doesn’t allow Apple ID so I can’t “restore purchase”. I purchased my subscription through App Store. Looking through the support documentation, it says to reach out to support. Happy to email my receipt when requested.
The unlock will work if you can sign in with your Agenda Account.
If you used Sign in with Apple, I guess it won’t work at your work because the iCloud account is not there.
What you can do is go to your home device, and into the Agenda Account section. If there is an email registered, you could sign out, type in the email, and then press “Reset Password”. You can then follow instructions to choose a password. At your work, you can then use the email + password to sign in, even without the iCloud account.
Let me know if that helps.