Gray globe (earth) appears after restart for no apparent reason - might something be wrong?

This is what happens when a Mac can’t find the internal bootable drive and falls back any NetBoot server, but there is no server to connect to.

You can reset your boot order by resetting the NVRAM. In the past this was called parameter RAM, which is why P and R are held down at startup.

• https://support.apple.com/en-us/HT204063

Network boot used to be a feature of OS X Server, then Server.app on macOS. Now Internet Recovery handles this for current hardware.

This means your Mac is trying to start up using files on your network instead of the copy of macOS on the hard drive which there is none so your Mac is stuck in a temporary loop.

When it's done, it gives up and boots from local files on the hard drive. Try turning on Airplane mode before the restart to prevent the globe from showing up.