The obvious thing to check is if you have FileVault enabled and attach a display simulator dongle. In the FileVault case, the machine does not restart to the OS but to a firmware / limited log in screen, but having a display connected won’t enable/disable FileVault.
You will want to have a remote KVM or someone that can log in for unexpected power failures. See this thread for a lot more options like power, display and management options for headless Macs.
Removing FileVault would allow the OS to boot fully in exchange for the data not being encrypted at rest.