We consider multi-robot systems under recurring tasks formalized as linear temporal logic (LTL) specifications. To solve the planning problem efficiently, we propose a bottom-up approach combining offline plan synthesis with online coordination, dynamically adjusting plans via real-time communication. To address action delays, we introduce a synchronization mechanism ensuring coordinated task execution, leading to a multi-agent coordination and synchronization framework that is adaptable to a wide range of multi-robot applications. The software package is developed in Python and ROS2 for broad deployment. We validate our findings through lab experiments involving nine robots showing enhanced adaptability compared to previous methods. Additionally, we conduct simulations with up to ninety agents to demonstrate the reduced computational complexity and the scalability features of our work.