Azure Front Door works across regions and support URL routing (HTTP(S)).
Note: HTTP(S) load-balancing services are Layer 7 load balancers that only accept HTTP(S) traffic. They are intended for web applications or other HTTP(S) endpoints. They include features such as SSL offload, web application firewall, path-based load balancing, and session affinity.

Incorrect:
Application Gateway and Azure Load Balancer only work within one single region.
Reference:
https://docs.microsoft.com/en-us/azure/architecture/guide/technology-choices/load-balancing-overview