You want to set up Exclaimer - Signatures for Google Workspace but would like to understand more about the implications on your existing third-party service's mail routing setup.
You have already configured Exclaimer - Signatures for Google Workspace alongside a third-party service and found that emails are routed directly to the third party and not to Exclaimer. Therefore, signatures are not applied to your emails.
It is possible to configure Exclaimer - Signatures for Google Workspace to work alongside another third-party service.
To achieve this, it is necessary to ensure that emails are routed to Exclaimer first, and once the emails are delivered back to Google Workspace, the emails route to the other third party.
With Google Workspace, there are various settings (such as Routing, Default Routing and Content Compliance) that can change the route of an email. Google doesn't currently offer any settings within the Admin Console to prioritize any of these rules; however, the order in which they were created determines the order in which they are processed.
If you have mail routing options configured for another third-party service, it is necessary to remove them and recreate the Routing, Default Routing and Content Compliance rules once the Content Compliance rule for Exclaimer has been created.