I'm running a function app in consumption mode and would like to know if all the assemblies packaged in an app are stored on an HDD or SSD? I'm seeing bad cold start times. If HDDs are being used, is there a way to upgrade to SSDs (without having to upgrade to a Premium plan)?
Azure Function is based on the App Service Sandbox. If you deploy it to azure, it will be deployed to a physical machine for storage and processing according to the virtual concept of service plan. If you use a Service Plan that Azure does not promise to give SSD durable storage, then your files will not be durable stored on the SSD. (Even if there is an SSD disk on the physical machine assigned to you, it will definitely not give you the SSD for durable storage.)
For example, your function app is based on a service plan, which requires Azure to allocate two virtual machines. Under these circumstances, no matter whether the actual physical machine has SSD or not, as long as the service plan you choose does not support SSD durable storage, then azure will not allocate your compiled files to the SSD disk for you to durable store(such as dll).
If you want to use SSDs for persistent storage, then you should choose a service plan that promises to provide persistent storage SSDs. Because the azure function is deployed to the machine based on the service plan.