The requirement for the data center servers to reach services in the cloud and services behind redistributed routes, along with the condition that the exit point toward the internet should only be propagated when there is a dynamically learned default route, necessitates the use of the 'default-information originate' OSPF feature.
This feature allows the advertisement of the default route in OSPF when it is present in the routing table, which is the case when it is dynamically learned from the upstream router.
References: The 'default-information originate' feature is part of OSPF configuration and is used to control the advertisement of default routes in an OSPF environment. This is further explained in the Cisco OSPF Configuration Guide, which details the use of this command to propagate default routes under certain conditions
https://learningnetwork.cisco.com/s/question/0D53i00000Kt544/defaultinformationoriginate-always