Regarding the issue of iOS Telegram not receiving push notifications in mainland China
Telegram cannot receive push notifications over cellular network; however, after connecting to Wi-Fi and enabling a global proxy, notifications can be received normally

Cause Analysis
Apple Push Notification service (APNs) uses different domains for different network environments:
Push channel under cellular network: courier2.push.apple.com — This domain currently has a fault/connection abnormality
Wi-Fi Push channel under network: courier.push.apple.com — This domain is currently connecting normally