I appreciate your efforts in designing a serverless REST API architecture using Azure components. However, I have concerns regarding the reliance on Cosmos DB as the global NoSQL database. While it provides multi-region support and scalability, the complexity of managing consistency and latency across regions can pose significant challenges in a production environment. Specifically, the default consistency model can lead to unexpected behavior if not configured properly, potentially exposing your application to stale reads or write conflicts. Additionally, the Application Gateway may introduce latency if not correctly configured for your traffic patterns, which could negate some benefits of a serverless architecture. I recommend considering the integration of Azure Monitor or Application Insights for better observability, as this will help you detect and troubleshoot issues in real-time. Lastly, I would suggest implementing robust security measures, such as API Management policies, to protect your endpoints against misuse. Overall, while the architecture is promising, these considerations must be addressed to ensure reliability and performance in production.