I wanted to update this question with an answer as I have finally landed on a path after spending several weeks with Azure Advisors on my Microsoft for Startups plan.
Looks like what I need is blue-green deployments:
https://learn.microsoft.com/en-us/azure/spring-apps/concepts-blue-green-deployment-strategies
And another valuable article that discusses "tagging" environments so Azure DevOps knows which one to deploy to:
https://learn.microsoft.com/en-us/azure/virtual-machines/linux/tutorial-azure-devops-blue-green-strategy