You do not need to generate separate app-specific passwords for each device. You may choose to use the same app-specific password for BusyCal across all your devices.
However, it is optional to generate a unique app-specific password for each device. This can help with organization and security since you can label each password for future reference. If needed, you can revoke a specific password without affecting others.
An app-specific password for BusyCal (or any app requiring iCloud access) is typically tied to the app itself, not the specific device. This means that you can use the same app-specific password on all three of your Apple devices running BusyCal.