I encountered the same issue trying to set the application and content storage subnet routing via Terraform to secure a storage account using the vnet.

https://learn.microsoft.com/en-us/azure/azure-functions/configure-networking-how-to?tabs=portal#3-enable-application-and-configuration-routing

As mentionned above, for the Application Routing, it is now available via the site_config block in Terraform

site_config {
    vnet_route_all_enabled            = true
}

Reference: https://learn.microsoft.com/en-us/azure/azure-functions/functions-app-settings#website_vnet_route_all

Application and some Configuration routing were available through the legacy app_settings in Terraform but it is NOT WORKING at least for me in 4.20.

"The existing WEBSITE_VNET_ROUTE_ALL app setting can still be used, and you can enable all traffic routing with either setting."

"The existing WEBSITE_CONTENTOVERVNET app setting with the value 1 can still be used, and you can enable routing through the virtual network with either setting."

https://learn.microsoft.com/en-us/azure/app-service/configure-vnet-integration-routing#configure-application-routing https://learn.microsoft.com/en-us/azure/azure-functions/functions-app-settings#website_contentovervnet

resource "azurerm_windows_function_app" "function_app" {
  ....
  app_settings = {
    .....
    "WEBSITE_VNET_ROUTE_ALL"                  = 1 #not working
    "WEBSITE_CONTENTOVERVNET"                 = 1 #not working
    ......
  }
  site_config {
        vnet_route_all_enabled            = true    #ok 
  }

 }