Implementations set forth herein relate an automated assistant that provides suggestion elements at an OEM application and/or third-party application that is accessible via an OEM vehicle computing device, which employs restrictions on communications between local applications. The automated assistant can render suggestions via OEM vehicle applications and/or third-party applications, and initialize actions for performance via the OEM vehicle applications and/or the third-party applications—despite the limitations. The suggestions can be rendered at a graphical user interface of a vehicle, and include content that, when spoken by a user, causes the automated assistant to initialize such actions. Actions that are suggested by the automated assistant can be performed by third-party applications that are different from a third-party application that is rendering the suggestion. In this way, a common automated assistant can be indiscriminately available via various vehicle computing devices, despite differences in restrictions of communications between vehicle applications.