K8s doesn't help you solve your geographical region problem, because the geographical region problem is not running appserver instances in multiple regions. Almost any PaaS will do that for you out of the box, with way less fuss than k8s. The hard part is distributing your data.

Less overhead than writing your own glue code, less overhead than learning Kubernetes, is just use a PaaS like Google App Engine, Amazon Elastic Beanstalk, Digital Ocean App Platform, or Heroku. You have access to the same distributed databases you would with k8s.

Cloud Run is PaaS for people that like Docker. If you don't even want to climb that learning curve, try one of the others.