There is currently no setting to define the signature for an automation rule - instead the AI looks for existing signatures for this property, prioritizing the signatures of the creator of the Automation rule.
If you wish to have a different signature for replies on one platform, you need to set up this rule with a dedicated user.
For example, one user (can be an existing one or created for this purpose) can save Google-specific signatures in the reply settings and then set up Google-specific automation rules, while another user can be used to configure automation rues for the other platforms where another signature should be used.