If there is no hypervisor involved we would consider that bare metal regardless of how automated the process of provisioning the system is (eg: packet.net, hetzner).
However, if we use your example then one is still managing the install process of the base system, updating it, patching it, securing it, managing application deployment on top, networking, etc.)
At the end of the day though that is still a layer below.
and unikernels also have a layer below because they are always run on hypervisors. Nobody is talking about true bare metal here, and you don't want to write your applications on true bare metal most of the time anyway. That's reserved for the situations where you really need to squeeze 110% out of your hardware, which will never be upgraded. A lot of older console games were written on true bare metal for this reason - I remember that on the Nintendo DS you could set up a DMA controller to copy a command buffer from main memory into the graphics processor's command FIFO, and another one to transfer sound samples, and there was a whole set of registers to select which VRAM bank was allocated to which purpose and whether the main graphics processor would be allocated to the top or bottom screen with the other one getting the secondary graphics processor - but web app servers are not in this situation.
However, if we use your example then one is still managing the install process of the base system, updating it, patching it, securing it, managing application deployment on top, networking, etc.)
At the end of the day though that is still a layer below.