If your main concern is user experience, you could upload an App_Offline.htm file to the root of your application that has a general message like "Undergoing website maintenance. Please try your request again in a few minutes." Then just remove it once the update is complete. More info here: https://www.learnrazorpages.com/publishing/publish-to-iis#locked-assemblies-and-app_offline-files

Another option may be to utilize Azure Deployment Slots. A deployment slot would allow you to deploy your site to a slot, then swap it without the site users ever noticing. Check out these links for more info:

https://docs.microsoft.com/en-us/azure/azure-functions/functions-deployment-slots

https://stackify.com/azure-deployment-slots