This happens because the affected users do not have the “API Enabled” system permission. While admins can access Apsona without issues, non-admin licensed users also require this permission to be enabled.
Solution:
Go to Setup → Profiles (or Permission Sets, if you are using them).
Open "System Permissions".
Enable "API Enabled" for the user’s profile or permission set.
Save the changes.
Clear browser cache or have the user re-login.
After these steps, users should be able to access Apsona successfully.